Traveling solitons in Lorentz-violating systems

TL;DR

This paper introduces a class of traveling solitons in Lorentz-violating systems, demonstrating their unique properties and providing a complete set of solutions that exhibit critical behavior influenced by an arbitrary constant.

Contribution

It presents the first construction of traveling solitons in Lorentz-violating models, which cannot be derived from static solutions via Lorentz boosts.

Findings

Complete set of traveling soliton solutions obtained.

Solutions exhibit critical behavior based on an arbitrary integration constant.

Traveling solitons cannot be mapped from static solutions due to Lorentz violation.

Abstract

In this work we present a class of traveling solitons in Lorentz-violating systems. In the case of Lorentz violating scenarios, it is usual to construct static solitonic configurations. Here it is shown that it is possible to construct some traveling solitons which, as it should be expected, can not be mapped into a static configuration by means of Lorentz boosts due to its explicit breaking. Furthermore, in the model studied, a complete set of solutions is obtained. The solutions present a critical behavior controlled by the choose of an arbitrary integration constant.