Kink-like solution for the Lorentz0violating \phi^4 theory equation of motion with dissipation

TL;DR

This paper derives an analytical kink-like solution for a Lorentz-violating  theory with dissipation, using a modified Hirota method to handle the nonlinear PDEs involved.

Contribution

It introduces a novel analytical approach to find kink solutions in Lorentz-violating  theories with dissipation, expanding the understanding of such nonlinear systems.

Findings

Analytical one-kink solution constructed for the Lorentz-violating  equation.

Modified Hirota method adapted for this nonlinear PDE.

Specific parameter conditions identified for the solution validity.

Abstract

A (1+1)-dimension equation of motion for \phi^4 theory is considered for the case of simultaneou taking into account the processes of dissipation and violation the Lorentz-invariance. A topological non-trivial solution of one-kink type for this equation is constructed in an analytical form. The modofied Hirota method for a solving the nonlinear partial differential equations is applied. A modification of the method led to the special conditions on parameters of the model and solution.