Dynamics of kinks in one- and two-dimensional hyperbolic models with quasidiscrete nonlinearities - art. no. 066613

We study the evolution of fronts in the Klein-Gordon equation when the nonl inear term is inhomogeneous. Extending previous works on homogeneous nonlin ear terms, we describe the derivation of an equation governing the front mo tion, which is strongly nonlinear, and, for the two-dimensional case, gener alizes the damped Born-Infeld equation. We study the motion of one- and two -dimensional fronts finding a much richer dynamics than in the homogeneous system case, leading, in most cases, to the stabilization of one phase insi de the other. For a one-dimensional front, the function describing the inho mogeneity of the nonlinear term acts as a "potential function" for the moti on of the front, i.e.. a front initially placed between two of its local ma xima asymptotically approaches the intervening minimum. Two-dimensional fro nts, with radial symmetry and without dissipation can either shrink to a po int in finite time, grow unboundedly, or their radius can oscillate, depend ing on the initial conditions. When dissipation effects are present, the os cillations either decay spirally or not depending on the value of the dampi ng dissipation parameter. For fronts with a more general shape, we present numerical simulations showing the same behavior.