2010•Journal of Yunyang Teachers CollegeRequires access

A New Method to Explicit Traveling Wave Solutions of the NLS Equation

YU Zhan-chi

Abstract

Deformation mapping method is applied to obtain exact solutions of the NLS equation.A simple algebraic transformation relation of a special type of solution between the NLS equation and the cubic nonlinear Klein-Gordon(NKG) equation is established.With the aid of this relation and known solutions of the NKG equation,abundant explicit and exact traveling wave solutions,which contain solitary wave solutions,periodic wave solutions,Jacobian elliptic function solutions and others exact solutions,are obtained.

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Key concepts: Elliptic function, Jacobian matrix and determinant, Mathematics, Traveling wave, Mathematical analysis, Transformation (genetics), Simple (philosophy), Nonlinear system