In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzent...In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.展开更多
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference...Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.展开更多
Through two methods, we investigate the solitary and periodic wave solutions of the differential equation describing a nonlinear coupled two-dimensional discrete electrical lattice. The fixed points of our model equat...Through two methods, we investigate the solitary and periodic wave solutions of the differential equation describing a nonlinear coupled two-dimensional discrete electrical lattice. The fixed points of our model equation are examined and the bifurcations of phase portraits of this equation for various values of the front wave velocity are presented. Using the sineGordon expansion method and classic integration, we obtain exact transverse solutions including breathers, bright solitons,and periodic solutions.展开更多
Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic ...Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear （2 ＋ 1） dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia Autonomous Region, Natural Science Foundation of Inner Mongolia Autonomous Region （Grant No 2004080201103） and the Youth Research Program of Inner Mongolia Normal University （Grant No QN005023）.
文摘In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the Natural Science Foundation （Grant No 200408020103）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia, China and the Youth Foundation （Grant No QN004024） of Inner Mongolia Normal University, China.
文摘Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.
文摘Through two methods, we investigate the solitary and periodic wave solutions of the differential equation describing a nonlinear coupled two-dimensional discrete electrical lattice. The fixed points of our model equation are examined and the bifurcations of phase portraits of this equation for various values of the front wave velocity are presented. Using the sineGordon expansion method and classic integration, we obtain exact transverse solutions including breathers, bright solitons,and periodic solutions.
基金the National Natural Science Foundation of China (10461006)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region (NJZZ07031)+1 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region (200408020103)the Natural Science Research Program of Inner Mongolia Normal University (QN005023)
文摘Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear （2 ＋ 1） dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.
