By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic functio...By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.展开更多
New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s pa...New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s parameters and travelling wave transformation parameters. Some figures for a specific kind of solution are also presented.展开更多
The modified mapping method is further improved by the expanded expression of u（ξ） that contains the terms of the first-order derivative of function f（ξ）. Some new exact solutions to the mBBM equation are determ...The modified mapping method is further improved by the expanded expression of u（ξ） that contains the terms of the first-order derivative of function f（ξ）. Some new exact solutions to the mBBM equation are determined by means of the method. We can obtain many new solutions in terms of the Jacobi elliptic functions of the equation.展开更多
A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the(2+1)-dimensional Broer-Kaup-Kupershmidt equation.Based on the variable separation solution and by selecting ...A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the(2+1)-dimensional Broer-Kaup-Kupershmidt equation.Based on the variable separation solution and by selecting appropriate functions,we discuss the completely elastic head-on collision between two dromion-lattices,non-completely elastic "chase and collision" between two multi-dromion-pairs and completely non-elastic interaction phenomenon between anti-dromion and dromion-pair.展开更多
With the help of a modified mapping method and a new mapping method, we re-study the （3＋1）-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions ...With the help of a modified mapping method and a new mapping method, we re-study the （3＋1）-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.展开更多
By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function so...By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.展开更多
With the help of a modified mapping method, we obtain two kinds of variable separation solutions with two arbitrary functions for the （24-1）-dimensional dispersive long wave equation. When selecting appropriate mult...With the help of a modified mapping method, we obtain two kinds of variable separation solutions with two arbitrary functions for the （24-1）-dimensional dispersive long wave equation. When selecting appropriate multi-valued functions in the variable separation solution, we investigate the interactions among special multi-dromions, dromion-like multi-peakons, and dromion-like multi-semifoldons, which all demonstrate non-completely elastic properties.展开更多
The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper w...The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the （2-1-1）-dimensional cubic Klein-Gordon （K-G） equation. The Klein-Gordon equations are relativistic version of Schr6dinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which several solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions of PDEs arise in mathematical physics.展开更多
基金Project supported by the State Key Program for Basic Research of China (Grant No 2004CB418304)the National Natural Science Foundation of China (Grant No 40405010)
文摘By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.
文摘New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s parameters and travelling wave transformation parameters. Some figures for a specific kind of solution are also presented.
基金The project supported by the Science and Technology Foundation of Cuizhou Province of China under Grant No. 20072009
文摘The modified mapping method is further improved by the expanded expression of u（ξ） that contains the terms of the first-order derivative of function f（ξ）. Some new exact solutions to the mBBM equation are determined by means of the method. We can obtain many new solutions in terms of the Jacobi elliptic functions of the equation.
基金Supported by the National Natural Science Foundation of China under Grant No. 11005092the Program for Innovative Research Team of Young Teachers under Grant No. 2009RC01Undergraduate Innovative Base of Zhejiang Agriculture and Forestry University,the Zhejiang Province Undergraduate Scientific and Technological Innovation Project under Grant No. 2012R412018
文摘A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the(2+1)-dimensional Broer-Kaup-Kupershmidt equation.Based on the variable separation solution and by selecting appropriate functions,we discuss the completely elastic head-on collision between two dromion-lattices,non-completely elastic "chase and collision" between two multi-dromion-pairs and completely non-elastic interaction phenomenon between anti-dromion and dromion-pair.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005092)the Undergraduate Scientific and Technological Innovation Project of Zhejiang Province of China (Grant No. 2012R412018)the Undergraduate Innovative Base Program of Zhejiang A & F University
文摘With the help of a modified mapping method and a new mapping method, we re-study the （3＋1）-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.
基金the State Key Basic Research Program of China under Grant No.2004CB418304
文摘By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.
基金Supported by the National Natural Science Foundation of China (Grant No. 11005092)the Program for Innovative Research Team of Young Teachers,China (Grant No. 2009RC01)+1 种基金the Undergraduate Innovative Base of Zhejiang A & F University,Chinathe Zhejiang Province Undergraduate Scientific and Technological Innovation Project,China (Grant No. 2012R412018)
文摘With the help of a modified mapping method, we obtain two kinds of variable separation solutions with two arbitrary functions for the （24-1）-dimensional dispersive long wave equation. When selecting appropriate multi-valued functions in the variable separation solution, we investigate the interactions among special multi-dromions, dromion-like multi-peakons, and dromion-like multi-semifoldons, which all demonstrate non-completely elastic properties.
文摘The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the （2-1-1）-dimensional cubic Klein-Gordon （K-G） equation. The Klein-Gordon equations are relativistic version of Schr6dinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which several solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions of PDEs arise in mathematical physics.
