Aim To calculate and analyze the near field distribution of ariborne short wave antenna. Methods B-spline method was used to get the mathermatital model of a Boeing 707320Baircraft and simulate its short wave antenna ...Aim To calculate and analyze the near field distribution of ariborne short wave antenna. Methods B-spline method was used to get the mathermatital model of a Boeing 707320Baircraft and simulate its short wave antenna . FDTD (finite-difference time-domain) method are ed tO complete the calculation and analysis. Results The near field distributions on aircraft's surface were obtained, the curve and gray figures of the normalized near field value were shown. Conclusion These modeling and calculating methods can provide data foraircraft's EMC analysis and design.展开更多
In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
Aict f Finjte rmvedrig wave (M) so1uhons fOr the fOllowhg sechear syttem (I){u_t-u_(xx)+u^mv^p=0 u_t-v_(xx)+u^q=0 -∞<x<+∞,t>0,p,q>0,m≥0 are studied. SolutiOns to (I) of the fOrm u (x, t)=lt(ct--x), v(...Aict f Finjte rmvedrig wave (M) so1uhons fOr the fOllowhg sechear syttem (I){u_t-u_(xx)+u^mv^p=0 u_t-v_(xx)+u^q=0 -∞<x<+∞,t>0,p,q>0,m≥0 are studied. SolutiOns to (I) of the fOrm u (x, t)=lt(ct--x), v(x, t)=v (cl--X) are called W soIutiOns if there exjstS a fwite ', such that u({)=v(j)=0 for t<{,':=ct--x. It is proVed that if Pq+nl<l, fOr any ed c thele erktS an FTW that is inhque up to phase transIahons and Is unbOunded, whena no rm ekist if pq+m> l. The asmpptohc weve profileS near the front as well as far from it are also determined. If I)q^m = l. the exjstence of travebe wave soluhons to (I) is proved. The plnof in Esqniruis's paper(1990) for the one m=0 co be sdriplified by using the methOd develOped in thjs paper.展开更多
A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutio...A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.展开更多
For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exa...For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the (2+l)-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.展开更多
This paper investigated the asymptotic behavior of global weak solutions of the initial boundary value problem for a class of nonlinear wave equations. Moreover, blowup of this kind of equations was also disscussed.
We study the WKB dispersion equation in non-uniform optical waveguide.There are three methods given in this paper:(1) method of Airy function;(2)method of connection formula;and(3) method of phase shift.At last we mak...We study the WKB dispersion equation in non-uniform optical waveguide.There are three methods given in this paper:(1) method of Airy function;(2)method of connection formula;and(3) method of phase shift.At last we make some remarks.展开更多
J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate...J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.展开更多
Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation m...Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.展开更多
In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm (CH) and Degasperis Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of...In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm (CH) and Degasperis Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.展开更多
In this paper, the simultaneous perturbation stochastic approximation (SPSA) algorithm is used for seeking optimal parameters in an adaptive filter developed for assimilating observations in the very high dimensiona...In this paper, the simultaneous perturbation stochastic approximation (SPSA) algorithm is used for seeking optimal parameters in an adaptive filter developed for assimilating observations in the very high dimensional dynamical systems. The main results show that the SPSA is capable of yielding the high filter performance similar to that produced by classical optimization algorithms, with better performance for non-linear filtering problems as more and more observations are assimilated. The advantage of the SPSA is that at each iteration it requires only two measurements of the objective function to approximate the gradient vector regardless of the dimension of the control vector (or maximally, three measurements if second-order optimization algorithms are used). The SPSA approach is thus free from the need to develop a discrete adjoint of tangent linear model as it is required up to now for solving optimization problems in very high dimensional systems. This technique offers promising perspectives on developing optimal assimilation systems encountered in the field of data assimilation in meteorology and oceanography.展开更多
This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the dis...This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the distance from the ship to the reference path always be within a specified value. The control design is based on a global exponential disturbance observer, a transformation of the ship dynamics to an almost spherical form, an interpretation of the tracking errors in an earth-fixed frame, an introduction of dynamic variables to compensate for relaxation of the reference path generation, p-times differentiable step functions, and backstepping and Lyapunov's direct methods. The effectiveness of the proposed results is illustrated through simulations.展开更多
The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuo...The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.展开更多
This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ i...This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →+∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.展开更多
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used ...Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.展开更多
The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment (given by the observation ...The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment (given by the observation process). The location and weight of each particle are governed by stochastic differential equations driven by the observation process, which is common for all particles, as well as by an individual Brownian motion, which applies to this specific particle only. The branching mechanism of each particle depends on the observation process and the path of this particle itself during its short lifetime δ = n-2α, where n is the number of initial particles and ~ is a fixed parameter to be optimized. As n → ∞, we prove the convergence of π to πt uniformly for t ∈ [0, T]. Compared with the available results in the literature, the main contribution of this article is that the approximation is free of any stochastic integral which makes the numerical implementation readily available.展开更多
This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar...This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t →∞. The convergence is uniform in Rn. Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system.展开更多
We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy le...We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.展开更多
文摘Aim To calculate and analyze the near field distribution of ariborne short wave antenna. Methods B-spline method was used to get the mathermatital model of a Boeing 707320Baircraft and simulate its short wave antenna . FDTD (finite-difference time-domain) method are ed tO complete the calculation and analysis. Results The near field distributions on aircraft's surface were obtained, the curve and gray figures of the normalized near field value were shown. Conclusion These modeling and calculating methods can provide data foraircraft's EMC analysis and design.
文摘In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
文摘Aict f Finjte rmvedrig wave (M) so1uhons fOr the fOllowhg sechear syttem (I){u_t-u_(xx)+u^mv^p=0 u_t-v_(xx)+u^q=0 -∞<x<+∞,t>0,p,q>0,m≥0 are studied. SolutiOns to (I) of the fOrm u (x, t)=lt(ct--x), v(x, t)=v (cl--X) are called W soIutiOns if there exjstS a fwite ', such that u({)=v(j)=0 for t<{,':=ct--x. It is proVed that if Pq+nl<l, fOr any ed c thele erktS an FTW that is inhque up to phase transIahons and Is unbOunded, whena no rm ekist if pq+m> l. The asmpptohc weve profileS near the front as well as far from it are also determined. If I)q^m = l. the exjstence of travebe wave soluhons to (I) is proved. The plnof in Esqniruis's paper(1990) for the one m=0 co be sdriplified by using the methOd develOped in thjs paper.
文摘A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, and the Key Academic Discipline of Zhejiang Province under Grant No. 200412.The authors are in debt to Prof. J.F. Zhang and Dr. W.H. Huang for their helpful suggestions and fruitful discussions.
文摘For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the (2+l)-dimenslonal dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns.
基金National Natural Science Foundation ofChina( No. 10 3 710 73 ) and Natural Science Foundation of HenanProvince( No.0 2 110 10 90 0 )
文摘This paper investigated the asymptotic behavior of global weak solutions of the initial boundary value problem for a class of nonlinear wave equations. Moreover, blowup of this kind of equations was also disscussed.
文摘We study the WKB dispersion equation in non-uniform optical waveguide.There are three methods given in this paper:(1) method of Airy function;(2)method of connection formula;and(3) method of phase shift.At last we make some remarks.
文摘J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.
基金The author would like to thank Profs. Jie-Fang Zhang and Chun-Long Zheng for helpful discussions.
文摘Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10771072, 10735030, and 90718041Shanghai Leading Academic Discipline Project under Grant No.B412
文摘In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm (CH) and Degasperis Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.
文摘In this paper, the simultaneous perturbation stochastic approximation (SPSA) algorithm is used for seeking optimal parameters in an adaptive filter developed for assimilating observations in the very high dimensional dynamical systems. The main results show that the SPSA is capable of yielding the high filter performance similar to that produced by classical optimization algorithms, with better performance for non-linear filtering problems as more and more observations are assimilated. The advantage of the SPSA is that at each iteration it requires only two measurements of the objective function to approximate the gradient vector regardless of the dimension of the control vector (or maximally, three measurements if second-order optimization algorithms are used). The SPSA approach is thus free from the need to develop a discrete adjoint of tangent linear model as it is required up to now for solving optimization problems in very high dimensional systems. This technique offers promising perspectives on developing optimal assimilation systems encountered in the field of data assimilation in meteorology and oceanography.
基金Supported in Part by the Australian Research Council Under Grant No.DP0988424
文摘This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the distance from the ship to the reference path always be within a specified value. The control design is based on a global exponential disturbance observer, a transformation of the ship dynamics to an almost spherical form, an interpretation of the tracking errors in an earth-fixed frame, an introduction of dynamic variables to compensate for relaxation of the reference path generation, p-times differentiable step functions, and backstepping and Lyapunov's direct methods. The effectiveness of the proposed results is illustrated through simulations.
基金supported by the National Natural Science Foundation of China under Grant Nos.10671184 and 10971203
文摘The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.
基金Project supported by Grant-in-Aid for Science Research (No.12740105, No.14204011), JSPS.
文摘This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →+∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.
基金Supported by the National Natural Science Foundation under Grant No. 11047010
文摘Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.
基金supported by US National Science Foundation(Grant No. DMS-0906907)
文摘The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment (given by the observation process). The location and weight of each particle are governed by stochastic differential equations driven by the observation process, which is common for all particles, as well as by an individual Brownian motion, which applies to this specific particle only. The branching mechanism of each particle depends on the observation process and the path of this particle itself during its short lifetime δ = n-2α, where n is the number of initial particles and ~ is a fixed parameter to be optimized. As n → ∞, we prove the convergence of π to πt uniformly for t ∈ [0, T]. Compared with the available results in the literature, the main contribution of this article is that the approximation is free of any stochastic integral which makes the numerical implementation readily available.
文摘This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t →∞. The convergence is uniform in Rn. Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system.
文摘We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.