Solitary waves in the coupled nonlinear massive Thirring as well as coupled Soler models with arbitrary nonlinearity

TL;DR

This paper introduces generalized coupled nonlinear models based on the Thirring and Soler equations, finds exact solitary wave solutions, and shows these solutions are conserved and relate to single-field solutions, with nonrelativistic limits matching one-component cases.

Contribution

It extends coupled Thirring and Soler models to arbitrary nonlinearity and derives exact solitary wave solutions, highlighting their invariance and relation to single-field solutions.

Findings

Exact solitary wave solutions for generalized models.

Solutions are independent of parameterization due to conservation laws.

Nonrelativistic reduction aligns with single-component solutions.

Abstract

Motivated by the recent introduction of an integrable coupled massive Thirring model by Basu-Mallick et al, we introduce a new coupled Soler model. Further we generalize both the coupled massive Thirring and the coupled Soler model to arbitrary nonlinear parameter $\kappa$ and obtain exact solitary wave solutions in both cases. Remarkably, it turns out that in both the models, because of the conservation laws of charge and energy, the exact solutions we find seem to not depend on how we parameterize them, and the charge density of these solutions is related to the charge density of the single field solutions found earlier by a subset of the present authors. In both the models, a nonrelativistic reduction of the equations leads to the same conclusion that the solutions are proportional to those found in the one component field case.