A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equati...A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.展开更多
In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is mo...In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 （2004） 1037]. Abundant new solutions o[ （2q-1）-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.展开更多
Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations （PDEs） with hyperbo...Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations （PDEs） with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation展开更多
In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with thr...In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential 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 of China
文摘A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions＇ soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 （2004） 1037]. Abundant new solutions o[ （2q-1）-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.
基金Supported by National Natural Science Foundation of China under Grant No.10926057 Foundation of Zhejiang Educational Committee under Grant No.Y200908784
文摘Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations （PDEs） with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101Key Disciplines of Shanghai Municipality under Grant No.S30104
文摘In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.
