Soliton, breather and shockwave solutions of the Heisenberg and the $T\bar T$ deformations of scalar field theories in 1+1 dimensions

TL;DR

This paper explores soliton, breather, and shockwave solutions in 1+1 dimensional scalar field theories, including Heisenberg's model and $Tar T$ deformations, providing explicit solutions and analyzing their properties.

Contribution

It presents explicit soliton solutions for deformed models, proves soliton mass invariance under $Tar T$ deformation, and conjectures breather solutions, advancing understanding of nonlinear wave solutions in these theories.

Findings

Explicit soliton solutions for sine-Gordon and Higgs potentials.

$Tar T$ deformation does not alter soliton mass.

Existence of shockwave solutions in deformed models.

Abstract

In this note we study soliton, breather and shockwave solutions in certain two dimensional field theories. These include: (i) Heisenberg's model suggested originally to describe the scattering of high energy nucleons (ii) $T\bar T$ deformations of certain canonical scalar field theories with a potential. We find explicit soliton solutions of these models with sine-Gordon and Higgs-type potentials. We prove that the $T\bar T$ deformation of a theory of a given potential does not correct the mass of the soliton of the undeformed one. We further conjecture the form of breather solutions of these models. We show that certain $T\bar T$ deformed actions admit shockwave solutions that generalize those of Heisenberg's Lagrangian.