Topologically non-trivial solution in a dissipative φ4 model with Lorentz-invariance violation

Abstract

In this paper a (1+1)-dimension equation of motion for φ4-theory is considered for the case of simultaneously taking into a account of 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. To this end, the modified direct Hirota method for solving the nonlinear partial derivatives equations was used. A modification of the method lead to special conditions on the parameters of the model and the solution.