Exact Explicit Solutions of Nonlinear Evolution Equation
Xu Chang-Zhi
Abstract
Xu Chang-Zhi
Abstract
In this work,a new direct ktruncatd approach for finding exact travelling wave solutions to nonlinear evolution equations is proposed and successfully applied to one generalized nonlinear physical models.Equations are reduced by using traveling wave method.A simple transformation relation are obtained by using leading order analysis and strating new form of nonlinear evolution equations.The abundant exact travelling wave solutions,which contain solitary wave solutions,periodic wave solutios,rational fraction solutions and Jacobian elliptic function solutions,are obtained by using extended function method and exact solutions of the cubic nonlinear Klein-Gordon equation.This method,a simple and effective,can also be apply to solve exact solutions of other nonlinear partial equation.
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In this work,a new direct ktruncatd approach for finding exact travelling wave solutions to nonlinear evolution equations is proposed and successfully applied to one generalized nonlinear physical models.Equations are reduced by using traveling wave method.A simple transformation relation are obtained by using leading order analysis and strating new form of nonlinear evolution equations.The abundant exact travelling wave solutions,which contain solitary wave solutions,periodic wave solutios,rational fraction solutions and Jacobian elliptic function solutions,are obtained by using extended function method and exact solutions of the cubic nonlinear Klein-Gordon equation.This method,a simple and effective,can also be apply to solve exact solutions of other nonlinear partial equation.
Key concepts: Elliptic function, Nonlinear system, Jacobian matrix and determinant, Simple (philosophy), Traveling wave, Mathematics, Mathematical analysis, Transformation (genetics)