Soliton solutions in two-dimensional Lorentz-violating higher derivative scalar theory

TL;DR

This paper develops a new analytical approach to find topological defect solutions in a 2D Lorentz-violating scalar field theory with higher derivatives, addressing complex equations of motion across different scenarios.

Contribution

It introduces a novel method for obtaining analytical solutions in higher-derivative Lorentz-violating scalar theories, applicable to various Lagrangians with complex equations.

Findings

Derived analytical topological defect solutions in three scenarios

Established constraints for dispersion relations in each scenario

Demonstrated the methodology's effectiveness despite equation complexity

Abstract

This paper shows a new approach to obtain analytical topological defects of a 2D Myers-Pospelov Lagrangian for two scalar fields. Such a Lagrangian presents higher-order kinetic terms, which lead us to equations of motion which are non-trivial to be integrated. Here we describe three possible scenarios for the equations of motion, named by timelike, spacelike and lightlike respectively. We started our investigation with a kink-like travelling wave Ansatz for the free theory, which led us to constraints for the dispersion relations of each scenario. We also introduced a procedure to obtain analytical solutions for the general theory in the three mentioned scenarios. We exemplified the procedure and discussed the behavior of the defect solutions carefully. It is remarkable that the methodology presented in this study led to analytical models, despite the complexity of the equations of motion derived from the 2D Myers-Pospelov Lagrangian. The methodology here tailored can be applied to several Lagrangians with higher-order derivative terms.