The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus vol...The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1:3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus (TMIB) power system.展开更多
In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. ...In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. Both the single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. Only the impermeable breakwaters are considered in this study. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with the appropriate mixed-type boundary conditions, and it is solved numerically using the ISBM. The numerical results are presented in terms of the hydrodynamic quantities of reflection and transmission coefficients. The values are first validated against the data of previous studies, computed, and discussed for a variety of structural conditions, including the height, width, and spacing of breakwater submergence. An excellent agreement is observed between the ISBM results and those of other methods. The breakwater width is found to feature marginal effects compared with the height. The present method is shown to accurately predict the resonant conditions at which the maximum reflection and transmission occur. The trapezoidal breakwaters are found to generally present a wide spectrum of reflections, suggesting that they would function better than the rectangular breakwaters. The dual breakwater systems are confirmed to perform much better than single structures.展开更多
In this paper, using the interpolation perturbation method. the author seeks tosolve several nonlinear problems. Numerical examples show that the method Df thispaper has good accuracy.
The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and ...The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.展开更多
The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes ...The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.展开更多
This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the...This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the SBM,the concept of the origin intensity factor(OIF)is introduced to avoid the singularities of the fundamental solutions.The SBM belongs to the meshless boundary collocation methods.The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently.Consequently,by using the SBM coupled with the CHIEF scheme and the self-regularization technique,the accuracy of the numerical solution can be improved,especially near the corresponding internal characteristic frequencies.Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method.The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.展开更多
In this paper,on the basis of Ref.[1],the author studies the boundary value problems of the second-order differential equations,the highest order derivatives of which contain the small parameters.The numerical example...In this paper,on the basis of Ref.[1],the author studies the boundary value problems of the second-order differential equations,the highest order derivatives of which contain the small parameters.The numerical examples show that the calculating process of this method is quite simple and its accuracy is even higher than that of the multiple scales method.展开更多
Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car followin...Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Kortewegde-Vries (KdV) equation and the modified Korteweg-de-Vries (mKdV) equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.展开更多
As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both b...As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both boundary element method(BEM) and meshless method. In this paper, the dual reciprocity method(DRM) is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function(RBF). Only randomly distributed nodes on the bounding surface of the domain are required and it doesn't need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.展开更多
This paper is taken up for the following difference equation problem (Pe);where e is a small parameter, c1, c2,constants and functions of k and e . Firstly, the case with constant coefficients is considered. Secondly,...This paper is taken up for the following difference equation problem (Pe);where e is a small parameter, c1, c2,constants and functions of k and e . Firstly, the case with constant coefficients is considered. Secondly, a general method based on extended transformation is given to handle (P.) where the coefficients may be variable and uniform asymptotic expansions are obtained. Finally, a numerical example is provided to illustrate the proposed method.展开更多
In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic be...In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.展开更多
In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
The two-component Camassa–Holm equation includes many intriguing phenomena. We propose a multi-symplectic compact method to solve the two-component Camassa–Holm equation. Based on its multi-symplectic formulation, t...The two-component Camassa–Holm equation includes many intriguing phenomena. We propose a multi-symplectic compact method to solve the two-component Camassa–Holm equation. Based on its multi-symplectic formulation, the proposed method is derived by the sixth-order compact finite difference method in spatial discretization and the symplectic implicit midpoint scheme in temporal discretization. Numerical experiments finely describe the velocity and density variables in the two-component integrable system and distinctly display the evolvement of the singular solutions. Moreover, the proposed method shows good conservative properties during long-time numerical simulation.展开更多
This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singula...This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.展开更多
The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the fr...The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.展开更多
The asymptotic behavior of solutions of a similarity equation for the laminar flow in a porous channel with suction at both expanding and contracting walls has been obtained by using a singular perturbation method.How...The asymptotic behavior of solutions of a similarity equation for the laminar flow in a porous channel with suction at both expanding and contracting walls has been obtained by using a singular perturbation method.However,in the matching process,this solution neglects exponentially small terms.To take into account these exponentially small terms,a method involving the inclusion of exponentially small terms in a perturbation series was used to find two of the solutions analytically.The series involving the exponentially small terms and expansion ratio predicts dual solutions.Furthermore,the result indicates that the expansion ratio has much important influence on the solutions.展开更多
The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of t...The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures.展开更多
The fluid flow induced by light-density, low-stiffness structures was treated as inviscid, incompressible irrotational and steady plane flow. On the basis of the dipole configuration method, a singularity distribution...The fluid flow induced by light-density, low-stiffness structures was treated as inviscid, incompressible irrotational and steady plane flow. On the basis of the dipole configuration method, a singularity distribution method of distributing sources/sinks and dipoles on interfaces of the structure and fluid was developed to solve the problem of fluid flow induced by the vibration of common structures, such as columns and columns with fins, deduce the expression of kinetic energy of the fluid flow, and obtain the added mass finally. The calculational instances with analytical solutions prove the reliability of this method.展开更多
Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method wa...Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.展开更多
A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms...A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms of the singular manifold is obtained. And localized structures are also investigated.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10632040)
文摘The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1:3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus (TMIB) power system.
基金supported by the Direction Général des Enseignements et de la Formation Supérieure of Algeria under Grant CNEPRU number G0301920140029
文摘In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. Both the single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. Only the impermeable breakwaters are considered in this study. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with the appropriate mixed-type boundary conditions, and it is solved numerically using the ISBM. The numerical results are presented in terms of the hydrodynamic quantities of reflection and transmission coefficients. The values are first validated against the data of previous studies, computed, and discussed for a variety of structural conditions, including the height, width, and spacing of breakwater submergence. An excellent agreement is observed between the ISBM results and those of other methods. The breakwater width is found to feature marginal effects compared with the height. The present method is shown to accurately predict the resonant conditions at which the maximum reflection and transmission occur. The trapezoidal breakwaters are found to generally present a wide spectrum of reflections, suggesting that they would function better than the rectangular breakwaters. The dual breakwater systems are confirmed to perform much better than single structures.
文摘In this paper, using the interpolation perturbation method. the author seeks tosolve several nonlinear problems. Numerical examples show that the method Df thispaper has good accuracy.
基金Project supported by the Program of the Key Laboratory of Rock and Soil Mechanics of Chinese Academy of Sciences (No.Z110507)
文摘The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
基金Work sponsored by"Ministero dell' University"CNR of Italy
文摘The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.
基金supported by the National Science Fund of China(Grant No.12122205)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper proposes amodified formulation of the singular boundarymethod(SBM)by introducing the combined Helmholtz integral equation formulation(CHIEF)and the self-regularization technique to exterior acoustics.In the SBM,the concept of the origin intensity factor(OIF)is introduced to avoid the singularities of the fundamental solutions.The SBM belongs to the meshless boundary collocation methods.The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently.Consequently,by using the SBM coupled with the CHIEF scheme and the self-regularization technique,the accuracy of the numerical solution can be improved,especially near the corresponding internal characteristic frequencies.Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method.The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.
文摘In this paper,on the basis of Ref.[1],the author studies the boundary value problems of the second-order differential equations,the highest order derivatives of which contain the small parameters.The numerical examples show that the calculating process of this method is quite simple and its accuracy is even higher than that of the multiple scales method.
基金supported by the National Basic Research Program of China (Grant No.2006CB705500)the National Natural Science Foundation of China (Grant Nos.10532060, 10602025, 10802042)the Natural Science Foundation of Ningbo (Grant No.2007A610050)
文摘Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Kortewegde-Vries (KdV) equation and the modified Korteweg-de-Vries (mKdV) equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.
基金Foundation item: Supported by the National Natural Science Foundation of China(50608036)
文摘As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both boundary element method(BEM) and meshless method. In this paper, the dual reciprocity method(DRM) is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function(RBF). Only randomly distributed nodes on the bounding surface of the domain are required and it doesn't need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.
文摘This paper is taken up for the following difference equation problem (Pe);where e is a small parameter, c1, c2,constants and functions of k and e . Firstly, the case with constant coefficients is considered. Secondly, a general method based on extended transformation is given to handle (P.) where the coefficients may be variable and uniform asymptotic expansions are obtained. Finally, a numerical example is provided to illustrate the proposed method.
文摘In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.
文摘In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570the Open Foundation of State Key Laboratory of High Performance Computing of China+1 种基金the Research Fund of the National University of Defense Technology under Grant No JC15-02-02the Fund from HPCL
文摘The two-component Camassa–Holm equation includes many intriguing phenomena. We propose a multi-symplectic compact method to solve the two-component Camassa–Holm equation. Based on its multi-symplectic formulation, the proposed method is derived by the sixth-order compact finite difference method in spatial discretization and the symplectic implicit midpoint scheme in temporal discretization. Numerical experiments finely describe the velocity and density variables in the two-component integrable system and distinctly display the evolvement of the singular solutions. Moreover, the proposed method shows good conservative properties during long-time numerical simulation.
基金supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
基金supported by the National Natural Science Foundation of China (Grant No. 50779008)
文摘The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.
文摘The asymptotic behavior of solutions of a similarity equation for the laminar flow in a porous channel with suction at both expanding and contracting walls has been obtained by using a singular perturbation method.However,in the matching process,this solution neglects exponentially small terms.To take into account these exponentially small terms,a method involving the inclusion of exponentially small terms in a perturbation series was used to find two of the solutions analytically.The series involving the exponentially small terms and expansion ratio predicts dual solutions.Furthermore,the result indicates that the expansion ratio has much important influence on the solutions.
文摘The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures.
文摘The fluid flow induced by light-density, low-stiffness structures was treated as inviscid, incompressible irrotational and steady plane flow. On the basis of the dipole configuration method, a singularity distribution method of distributing sources/sinks and dipoles on interfaces of the structure and fluid was developed to solve the problem of fluid flow induced by the vibration of common structures, such as columns and columns with fins, deduce the expression of kinetic energy of the fluid flow, and obtain the added mass finally. The calculational instances with analytical solutions prove the reliability of this method.
基金Supported by the National Natural Science Foundation of China under Grant No.50921001973 Program under Grant No. 2010CB83270
文摘Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.
基金Supported by Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070486094
文摘A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms of the singular manifold is obtained. And localized structures are also investigated.