With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to （2＋1）-dimensional Toda system are obtained. The method used...With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to （2＋1）-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.展开更多
In this paper, we establish a priori estimates to the generalized second order Toda system{-Δu1（x）=2R1（x）eu1-R2eu2,-Δu2（x）=R1（x）eu1＋2R2eu2 in R2 , and discuss the convergence and asymptotic behavior of its ...In this paper, we establish a priori estimates to the generalized second order Toda system{-Δu1（x）=2R1（x）eu1-R2eu2,-Δu2（x）=R1（x）eu1＋2R2eu2 in R2 , and discuss the convergence and asymptotic behavior of its solutions, where Ri（x）, i=1, 2, is bounded function in R2 . Consequently, we prove that all the solutions satisfy an identity, which is somewhat a generalization of the well-known Kazdan-Warner condition.展开更多
In this paper, we study the solutions for Toda system on Riemann surface with boundary. We prove a sufficient condition for the existence of solution of Toda system in the critical case.
In this paper,we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs.Our method is based on calculus of variations,which was built on connect...In this paper,we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs.Our method is based on calculus of variations,which was built on connected finite graphs by Grigor'yan,Lin and Yang.展开更多
In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （...In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （DDEs）, As a concrete example, new families of exact solutions to the （2＋1）-dimensional Toda lattice system are obtained by the extended projective approach.展开更多
By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of ...By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the （2＋1）- dimensional Toda lattice hierarchy are given. Finally, the （2＋1）-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.展开更多
In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results...In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations.展开更多
The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions ...The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.展开更多
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province.
文摘With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to （2＋1）-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.
基金Supported by National Natural Science Foundation of China (Grant No. 10671156)
文摘In this paper, we establish a priori estimates to the generalized second order Toda system{-Δu1（x）=2R1（x）eu1-R2eu2,-Δu2（x）=R1（x）eu1＋2R2eu2 in R2 , and discuss the convergence and asymptotic behavior of its solutions, where Ri（x）, i=1, 2, is bounded function in R2 . Consequently, we prove that all the solutions satisfy an identity, which is somewhat a generalization of the well-known Kazdan-Warner condition.
基金Supported by National Natural Science Foundation of China （Grant No. 11001268）
文摘In this paper, we study the solutions for Toda system on Riemann surface with boundary. We prove a sufficient condition for the existence of solution of Toda system in the critical case.
基金partially supported by the National Science Foundation of China(Grant No.11401575 and 11721101).
文摘In this paper,we study existence of solutions of mean field equations for the equilibrium turbulence and Toda systems on connected finite graphs.Our method is based on calculus of variations,which was built on connected finite graphs by Grigor'yan,Lin and Yang.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang LishuiThe authors are in debt to Profs. J.F. Zhang, Z.M. Sheng, and L.Q. Chen, Drs. Z.Y. Ma and W.H. Huang for their helpful suggestions and fruitful discussions, and express their sincere thanks to Prof. S.Y. Lou for his useful references.University under Grant No. KZ05010
文摘In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （DDEs）, As a concrete example, new families of exact solutions to the （2＋1）-dimensional Toda lattice system are obtained by the extended projective approach.
基金supported by the State Key Basic Research Development Program of China under Grant No.2004CB318000
文摘By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the （2＋1）- dimensional Toda lattice hierarchy are given. Finally, the （2＋1）-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.
基金Supported by Leading Academic Discipline Program, 211 Project for Shanghai University of Finance and Economics (the 3rd phase)
文摘In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations.
基金the National Natural Science Foundation of China(Grant Nos.12061051 and 11965014)。
文摘The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.
