Solution of the asymmetric double sine-Gordon equation

TL;DR

This paper introduces a method using Mobius transformation to find solutions of the asymmetric double sine-Gordon equation across its entire parameter space, revealing phase transitions and deconfinement phenomena.

Contribution

The authors develop a comprehensive approach to solve the asymmetric double sine-Gordon equation for all parameter values, including phase transitions and solution classifications.

Findings

Solutions characterized for all  values of \u03c6.

Identification of deconfinement near specific  values.

Prediction of different solution types and phase transitions.

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 \phi-\eta parameter plane where \phi is an additional phase and \eta is the ratio of the magnitudes of two sine terms. We are able to show how the deconfinement occurs near \phi=(1/2+n)\pi and \phi=n pi. and also find the solution for all values of \phi. We predict different kind of solutions and transitions among them in different parts of the parameter space of this equation.