Dynamics of Kinks in One- and Two- Dimensional Hyperbolic Models with Quasi-Discrete Nonlinearities

Abstract

We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is non-homogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts, finding that the dynamics is richer than in the homogeneous reaction term case.