Analytical methods of asymmetry double sine-Gordon equation in infinite one-dimensional system

Abstract

Traditionally, Double Sine-Gordon Equation (DSGE) is seen as a nonintegrable equation. That means we cannot find general solutions in asymmetry DSGE. In this paper, we develop analytical method to solve this equation by Mobius transformation. And finally, this can reduce the problem to find roots of polynomial of four degree in one element. We have known this can be solved by square formally because its degree less than five. Although complexity as a solution, but in this sense, we can say we formally solve this nonintegrable equation.