Author(s)

Lina Yi, Jundong Bao,   Taogetusang^*

College of Mathematical Science, Inner Mongolia Normal University, Inner Mongolia, China.

The method combining the function transformation with the auxiliary equation is presented and the new infinite sequence complexion solutions of a class of nonlinear evolutionary equations are constructed. Step one, according to two function transformations, a class of nonlinear evolutionary equations is changed into two kinds of ordinary differential equations. Step two, using the first integral of the ordinary differential equations, two first order nonlinear ordinary differential equations are obtained. Step three, using function transformation, two first order nonlinear ordinary differential equations are changed to the ordinary differential equation that could be integrated. Step four, the new solutions, Bäcklund transformation and the nonlinear superposition formula of solutions of the ordinary differential equation that could be integrated are applied to construct the new infinite sequence complexion solutions of a class of nonlinear evolutionary equations. These solutions are consisting of two-soliton solutions, two-period solutions and solutions composed of soliton solutions and period solutions.

Nonlinear Evolutionary Equation, Function Transformation, Nonlinear Superposition Formula of Solutions, Complexion New Solutions

Yi, L. , Bao, J. and Taogetusang, &. (2015) The New Infinite Sequence Complexion Solutions of a Kind of Nonlinear Evolutionary Equations. Journal of Applied Mathematics and Physics, 3, 1624-1632. doi: 10.4236/jamp.2015.312187.