Generalized MSTB Models: Structure and kink varieties

TL;DR

This paper explores a broad class of two-component scalar field models in (1+1) dimensions, generalizing the MSTB model, and provides a systematic way to identify solitary wave solutions as trajectories in an equivalent mechanical system.

Contribution

It introduces a systematic procedure to characterize generalized MSTB models and identify kink solutions via mechanical analogies, extending the understanding of these models.

Findings

Characterization of a class of generalized MSTB models.

Identification of kink solutions as homoclinic or heteroclinic trajectories.

Application to a specific polynomial potential energy density.

Abstract

In this paper we describe the structure of a class of two-component scalar field models in a (1+1) Minkowskian space-time which generalize the well-known Montonen-Sarker-Trullinger-Bishop -hence MSTB- model. This class includes all the field models whose static field equations are equivalent to the Newton equations of two-dimensional type I Liouville mechanical systems with a discrete set of instability points. We offer a systematic procedure to characterize these models and to identify the solitary wave or kink solutions as homoclinic or heteroclinic trajectories in the analogous mechanical system. This procedure is applied to a one-parametric family of generalized MSTB models with a degree-eight polynomial as potential energy density.