Author(s)

Yu Mei Bai¹, Taogetusang  ^1,2

¹The College of Mathematical, Inner Mongolia University for Nationalities, Tongliao, China.
²College of Mathematical Science, Inner Mongolia Normal University, Huhhot, China.

By the function transformation and the first integral of the ordinary differential equations, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is researched, and the new solutions are obtained. First, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is changed to the problem of solving the solutions of the nonlinear ordinary differential equation. Second, with the help of the B?cklund transformation and the nonlinear superposition formula of solutions of the first kind of elliptic equation and the Riccati equation, the new infinite sequence soliton-like solutions of two kinds of sine-Gordon equations are constructed.

First Integral, Multiple Sine-Gordon Equation, Bäcklund Transformation, New Infinite Sequence Soliton-Like Solutions

Bai, Y. and  , T. (2016) The New Infinite Sequence Solutions of Multiple Sine-Gordon Equations. Journal of Applied Mathematics and Physics, 4, 796-805. doi: 10.4236/jamp.2016.44090.