Abstract
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, Backlund 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.
Highlights
In Refs. [1]-[5], some methods were applied to research the following two nonlinear coupling systems, and a finite number of one soliton solutions were obtained.How to cite this paper: Yi, L.N., Bao, J.D. and Taogetusang (2015) The New Infinite Sequence Complexion Solutions of a Kind of Nonlinear Evolutionary Equations
The new solutions, Bäcklund transformation and the nonlinear superposition formula of solutions of the ordinary differential equation that could be integrated [10]-[12] are applied to construct the new infinite sequence complexion solutions consisting of the Riemann θ function, the Jacobi elliptic function, the hyperbolic function, the trigonometric function and the rational function of a class of nonlinear evolutionary equations (10)
With the help of the relative conclusions of the second kind of elliptic equation [11]-[13], by analyzing, the infinite sequence solutions of the ordinary differential Equations (35) and (36) are obtained. Substituting these solutions into function transformation (44) yields the new infinite sequence complexion solutions consisting of the Riemann θ function, the Jacobi elliptic function, the hyperbolic function, the trigonometric function and the rational function of a class of nonlinear evolutionary Equation (10) in some kinds of cases
Summary
In Refs. [1]-[5], some methods were applied to research the following two nonlinear coupling systems, and a finite number of one soliton solutions were obtained. The new solutions, Bäcklund transformation and the nonlinear superposition formula of solutions of the ordinary differential equation that could be integrated [10]-[12] are applied to construct the new infinite sequence complexion solutions consisting of the Riemann θ function, the Jacobi elliptic function, the hyperbolic function, the trigonometric function and the rational function of a class of nonlinear evolutionary equations (10). These solutions are consisting of two-soliton solutions, two-period solutions and solutions composed of soliton solutions and period solutions. Α j , βi (i= j= 1, 2,⋅⋅⋅, 7),γ1,γ 2 ,δ1,δ2 are constants
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