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

摘要

This paper shows a new approach to obtain analytical topological defects fora 2D Myers-Pospelov Lagrangian for two scalar fields. Such a Lagrangianpresents higher-order kinetic terms, which lead us to equations of motion whichare non-trivial to be integrated. Here we describe three possible scenarios forthe equations of motion, named by time-like, space-like and light-likerespectively. We started our investigation with a kink-like travelling waveAnsatz for the free theory, which led us to constraints for the dispersionrelations of each scenario. We also introduced a method to obtain analyticalsolution for the general theory in the three mentioned scenarios. Weexemplified the method and discussed the behavior of the defects solutions.