In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.展开更多
The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling w...The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation method.Many novel soliton solutions are extracted using these methods.Furthermore,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica.The constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena.展开更多
This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational funct...This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.展开更多
In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which...In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.展开更多
In this paper, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. We study the (2+1)-dimensional BKP...In this paper, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. We study the (2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions. The method used here can be also extended to other nonlinear partial differential equations.展开更多
In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new typ...In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new types of periodic wave solutions which are rarely found in previous studies. As <em>m</em> → 0 and <em>m</em> → 1, some new types of trigonometric solutions and solitary solutions are also obtained correspondingly. This method is promising for constructing abundant periodic wave solutions and solitary solutions of nonlinear evolution equations (NLEEs) in mathematical physics.展开更多
In this paper, an efficient approximated method based upon the method of auxiliary sources (MAS) is proposed to solve the two-dimensional scattering problem of large, infinite dielectric cylinder. To reduce the size...In this paper, an efficient approximated method based upon the method of auxiliary sources (MAS) is proposed to solve the two-dimensional scattering problem of large, infinite dielectric cylinder. To reduce the size of the total computational cost, the formulation of the MAS is modified by minimizing the number of auxiliary sources considered to implement the solution. It is shown that the standard formulation of the method of auxiliary sources, based on placing a finite number of auxiliary sources in an interior cylinder and the same number in the exterior cylinder surrounding the physical boundary, can be replaced by a finite number of strips placed on the same interior and exterior cylinder. These strips, containing auxiliary sources, are separated by a constant angle. Thus, compared with the standard MAS, the number of auxiliary sources of the new approximated method is reduced; also the proposed method can greatly reduce the computational complexity and the memory requirement. The numerical results obtained in this paper reveal the validity of the proposed approximated method.展开更多
By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for general...By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations.展开更多
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are...In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.展开更多
With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G′/G-expansion met...With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G′/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.展开更多
The Sasa-satsuma(SS)dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers.This dynamical model has important physical significance.In this article,two mathematical technique...The Sasa-satsuma(SS)dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers.This dynamical model has important physical significance.In this article,two mathematical techniques namely,improved F-expansion and improved aux-iliary methods are utilized to construct the several types of solitons such as dark soliton,bright soliton,periodic soliton,Elliptic function and solitary waves solutions of Sasa-satsuma dynamical equation.These results have imperative applications in sciences and other fields,and construc-tive to recognize the physical structure of this complex dynamical model.The computing work and obtained results show the infuence and effectiveness of current methods.展开更多
In this paper, the nonlinear dispersive Zakharov- Kuznetsov equation is solved by using the generalized auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions ...In this paper, the nonlinear dispersive Zakharov- Kuznetsov equation is solved by using the generalized auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found.展开更多
In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique...In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique.Considering the Lie invariance condition,we find the symmetry generators.The pro-posed model yields eight-dimensional Lie algebra.Moreover,an optimal system of sub-algebras is com-puted,and similarity reductions are made.The considered nonlinear partial differential equation is re-duced into ordinary differential equations(ODEs)by utilizing the similarity transformation method(STM),which has the benefit of yielding a large number of accurate traveling wave solutions.These ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases,while in other cases,we use the new auxiliary equation method to get its soliton solutions.The evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.展开更多
A second order accurate(in time)numerical scheme is analyzed for the slope-selection(SS)equation of the epitaxial thin film growth model,with Fourier pseudo-spectral discretization in space.To make the numerical schem...A second order accurate(in time)numerical scheme is analyzed for the slope-selection(SS)equation of the epitaxial thin film growth model,with Fourier pseudo-spectral discretization in space.To make the numerical scheme linear while preserving the nonlinear energy stability,we make use of the scalar auxiliary variable(SAV)approach,in which a modified Crank-Nicolson is applied for the surface diffusion part.The energy stability could be derived a modified form,in comparison with the standard Crank-Nicolson approximation to the surface diffusion term.Such an energy stability leads to an H2 bound for the numerical solution.In addition,this H2 bound is not sufficient for the optimal rate convergence analysis,and we establish a uniform-in-time H3 bound for the numerical solution,based on the higher order Sobolev norm estimate,combined with repeated applications of discrete H¨older inequality and nonlinear embeddings in the Fourier pseudo-spectral space.This discrete H3 bound for the numerical solution enables us to derive the optimal rate error estimate for this alternate SAV method.A few numerical experiments are also presented,which confirm the efficiency and accuracy of the proposed scheme.展开更多
The main objective of this study is to nd novel wave solutions for the time-fractional generalized Rosenau-Kawahara-RLW equation,which occurs in unidirectional water wave prop-agation.The generalized Rosenau-Kawahara-...The main objective of this study is to nd novel wave solutions for the time-fractional generalized Rosenau-Kawahara-RLW equation,which occurs in unidirectional water wave prop-agation.The generalized Rosenau-Kawahara-RLW equation comprises three equations Rosenau equation,Kawahara equation,RLW equation and also p-th order nonlinear term.All these equations describe the wave phenomena especially the wave-wave and wave-wall interactions in shallow and narrow channel waters.The auxiliary equation method is employed to get the analytical results.展开更多
This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differenti...This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.展开更多
It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous...It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous other unknown solutions and physical attributes for the nonlinear models,as well as for the benefit of the largest audience feasible.To achieve this goal,we propose a new extended unified auxiliary equation technique,a brand-new analytical method for solving nonlinear partial differential equations.The proposed method is applied to the nonlinear Schrödinger equation with a higher dimension in the anomalous dispersion.Many interesting solutions have been obtained.Moreover,to shed more light on the features of the obtained solutions,the figures for some obtained solutions are graphed.The propagation characteristics of the generated solutions are shown.The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values.It is worth noting that the new method is very effective and efficient,and it may be applied in the realisation of novel solutions.展开更多
Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equat...Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other (l+l)-dimensional and higher dimensional systems.展开更多
In the present study,the solitary wave solutions of modified Degasperis-Procesi equation are developed.Unlike the standard Degasperis-Procesi equation,where multi-peakon solutions arise,the modification caused a chang...In the present study,the solitary wave solutions of modified Degasperis-Procesi equation are developed.Unlike the standard Degasperis-Procesi equation,where multi-peakon solutions arise,the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped solitons.By using the extended auxiliary equation method,we deduced some new soliton solutions of the fourthorder nonlinear modified Degasperis-Procesi equation with constant coefficient.These solutions include symmetrical,non-symmetrical kink solutions,solitary pattern solutions,weiestrass elliptic function solutions and triangular function solutions.We discuss the stability analysis for these solutions.展开更多
In this paper, the higher order NLS equation with cubic-quintic nonlinear terms is studied, new abundant solitary solutions with traveling-wave envelope of this equation are obtained with the aid of a generalized auxi...In this paper, the higher order NLS equation with cubic-quintic nonlinear terms is studied, new abundant solitary solutions with traveling-wave envelope of this equation are obtained with the aid of a generalized auxiliary equation method and complex envelope non-traveling transform approach.展开更多
文摘In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.
文摘The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation method.Many novel soliton solutions are extracted using these methods.Furthermore,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica.The constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena.
基金Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010B17914) and the National Natural Science Foundation of China (Grant No. 10926162).
文摘This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.
基金supported by the National Natural Science Foundation of China (No.10461005)the Ph.D.Programs Foundation of Ministry of Education of China (No.20070128001)the High Education Science Research Program of Inner Mongolia (No.NJZY08057)
文摘In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.
基金Foundation item: Supported by the National Natural Science Foundation of China(10647112)
文摘In this paper, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. We study the (2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions. The method used here can be also extended to other nonlinear partial differential equations.
文摘In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new types of periodic wave solutions which are rarely found in previous studies. As <em>m</em> → 0 and <em>m</em> → 1, some new types of trigonometric solutions and solitary solutions are also obtained correspondingly. This method is promising for constructing abundant periodic wave solutions and solitary solutions of nonlinear evolution equations (NLEEs) in mathematical physics.
文摘In this paper, an efficient approximated method based upon the method of auxiliary sources (MAS) is proposed to solve the two-dimensional scattering problem of large, infinite dielectric cylinder. To reduce the size of the total computational cost, the formulation of the MAS is modified by minimizing the number of auxiliary sources considered to implement the solution. It is shown that the standard formulation of the method of auxiliary sources, based on placing a finite number of auxiliary sources in an interior cylinder and the same number in the exterior cylinder surrounding the physical boundary, can be replaced by a finite number of strips placed on the same interior and exterior cylinder. These strips, containing auxiliary sources, are separated by a constant angle. Thus, compared with the standard MAS, the number of auxiliary sources of the new approximated method is reduced; also the proposed method can greatly reduce the computational complexity and the memory requirement. The numerical results obtained in this paper reveal the validity of the proposed approximated method.
基金The project supported by the Natural Science Foundation of Anhui Province of China under Grant No. 01041188 and the Foundation of Classical Courses of Anhui Province
文摘By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations.
基金Project supported by the Anhui Key Laboratory of Information Materials and Devices (Anhui University),China
文摘In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.
文摘With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher's equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G′/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.
文摘The Sasa-satsuma(SS)dynamical equation interpret propagation of ultra-short and femto-second pulses in optical fibers.This dynamical model has important physical significance.In this article,two mathematical techniques namely,improved F-expansion and improved aux-iliary methods are utilized to construct the several types of solitons such as dark soliton,bright soliton,periodic soliton,Elliptic function and solitary waves solutions of Sasa-satsuma dynamical equation.These results have imperative applications in sciences and other fields,and construc-tive to recognize the physical structure of this complex dynamical model.The computing work and obtained results show the infuence and effectiveness of current methods.
基金supported by the National Natural Science Foundation of China under Grant No.10647112the Foundation of Donghua University
文摘In this paper, the nonlinear dispersive Zakharov- Kuznetsov equation is solved by using the generalized auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found.
基金The authors would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project R-2022-178.
文摘In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique.Considering the Lie invariance condition,we find the symmetry generators.The pro-posed model yields eight-dimensional Lie algebra.Moreover,an optimal system of sub-algebras is com-puted,and similarity reductions are made.The considered nonlinear partial differential equation is re-duced into ordinary differential equations(ODEs)by utilizing the similarity transformation method(STM),which has the benefit of yielding a large number of accurate traveling wave solutions.These ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases,while in other cases,we use the new auxiliary equation method to get its soliton solutions.The evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.
文摘A second order accurate(in time)numerical scheme is analyzed for the slope-selection(SS)equation of the epitaxial thin film growth model,with Fourier pseudo-spectral discretization in space.To make the numerical scheme linear while preserving the nonlinear energy stability,we make use of the scalar auxiliary variable(SAV)approach,in which a modified Crank-Nicolson is applied for the surface diffusion part.The energy stability could be derived a modified form,in comparison with the standard Crank-Nicolson approximation to the surface diffusion term.Such an energy stability leads to an H2 bound for the numerical solution.In addition,this H2 bound is not sufficient for the optimal rate convergence analysis,and we establish a uniform-in-time H3 bound for the numerical solution,based on the higher order Sobolev norm estimate,combined with repeated applications of discrete H¨older inequality and nonlinear embeddings in the Fourier pseudo-spectral space.This discrete H3 bound for the numerical solution enables us to derive the optimal rate error estimate for this alternate SAV method.A few numerical experiments are also presented,which confirm the efficiency and accuracy of the proposed scheme.
文摘The main objective of this study is to nd novel wave solutions for the time-fractional generalized Rosenau-Kawahara-RLW equation,which occurs in unidirectional water wave prop-agation.The generalized Rosenau-Kawahara-RLW equation comprises three equations Rosenau equation,Kawahara equation,RLW equation and also p-th order nonlinear term.All these equations describe the wave phenomena especially the wave-wave and wave-wall interactions in shallow and narrow channel waters.The auxiliary equation method is employed to get the analytical results.
文摘This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.
文摘It is commonly recognized that,despite current analytical approaches,many physical aspects of nonlinear models remain unknown.It is critical to build more efficient integration methods to design and construct numerous other unknown solutions and physical attributes for the nonlinear models,as well as for the benefit of the largest audience feasible.To achieve this goal,we propose a new extended unified auxiliary equation technique,a brand-new analytical method for solving nonlinear partial differential equations.The proposed method is applied to the nonlinear Schrödinger equation with a higher dimension in the anomalous dispersion.Many interesting solutions have been obtained.Moreover,to shed more light on the features of the obtained solutions,the figures for some obtained solutions are graphed.The propagation characteristics of the generated solutions are shown.The results show that the proper physical quantities and nonlinear wave qualities are connected to the parameter values.It is worth noting that the new method is very effective and efficient,and it may be applied in the realisation of novel solutions.
基金Supported by the National Natural Science Foundation of China (No. 10647112)the Foundation of Donghua University
文摘Based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method, the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations. New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple. The method is also valid for other (l+l)-dimensional and higher dimensional systems.
文摘In the present study,the solitary wave solutions of modified Degasperis-Procesi equation are developed.Unlike the standard Degasperis-Procesi equation,where multi-peakon solutions arise,the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped solitons.By using the extended auxiliary equation method,we deduced some new soliton solutions of the fourthorder nonlinear modified Degasperis-Procesi equation with constant coefficient.These solutions include symmetrical,non-symmetrical kink solutions,solitary pattern solutions,weiestrass elliptic function solutions and triangular function solutions.We discuss the stability analysis for these solutions.
基金Supported by the National Natural Science Foundation of China(No.11361048)
文摘In this paper, the higher order NLS equation with cubic-quintic nonlinear terms is studied, new abundant solitary solutions with traveling-wave envelope of this equation are obtained with the aid of a generalized auxiliary equation method and complex envelope non-traveling transform approach.