Coupled Sine-Gordon and $\phi^4$ System

TL;DR

This paper investigates a coupled sine-Gordon and phi^4 system, demonstrating that coupling can impart stability to the phi^4 system's solutions, which are typically non-solitonic and unstable.

Contribution

It introduces a novel coupling of sine-Gordon and phi^4 systems and shows how this coupling can stabilize phi^4 solutions.

Findings

Coupling imparts stability to phi^4 solutions.

Sine-Gordon coupling influences soliton behavior.

Partial success in stabilizing non-solitonic solutions.

Abstract

Coupling the fields may lead to the emergence of new phenomena. In the realm of classical fields and nonlinear systems, extensive research has been conducted on their solitary and soliton solutions. In the conducted studies, typically two $\phi^4$ systems, or two sine-Gordon systems, have been coupled. The sine-Gordon system exhibits diverse solutions, all well-behaved, with its soliton solutions fully understood. On the other hand, the $\phi^4$ system, which is significant in field theory, has solitary solutions, but these solutions are not solitonic. For example, from a pair of kink and antikink, we cannot construct a bound state; or that after a collision, these two solutions do not revert to their initial status and become disrupted. In this study, we couple a $\phi^4$ system with a sine-Gordon system to impart stability from the sine-Gordon system to the $\phi^4$ system. We have demonstrated that for a coupled $\phi^4$ and sine-Gordon system, this expectation is somewhat met.