Solution of the asymmetric double sine-Gordon equation

Abstract

We present solutions of asymmetric double sine-Gordon equation (DSGE) of an infinite system based on Mobius transformation and numerical exercise. This method is able to give the forms of the solutions for all the region on the ϕ-ηparameter plane where ϕis an additional phase and ηis the ratio of the magnitudes of two sine terms. We are able to show how the deconfinement occurs near ϕ=(1/2+n)πand ϕ=n pi. and also find the solution for all values of ϕ. We predict different kind of solutions and transitions among them in different parts of the parameter space of this equation.

21 pages, 10 figures