Dynamics of kinks in one- and two-dimensional hyperbolic models with quasidiscrete nonlinearities
We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is inhomogeneous. 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 a much richer dynamics than in the homogeneous system case, leading, in most cases, to the stabilization of one phase inside the other. For a one-dimensional front, the function describing the inhomogeneity of the nonlinear term acts as a {open_quotes}potential function{close_quotes} for the motion of the front, i.e., a front initially placed between two of its local maxima asymptotically approaches the intervening minimum. Two-dimensional fronts, with radial symmetry and without dissipation can either shrink to a point in finite time, grow unboundedly, or their radius can oscillate, depending on the initial conditions. When dissipation effects are present, the oscillations either decay spirally or not depending on the value of the damping dissipation parameter. For fronts with a more general shape, we present numerical simulations showing the same behavior.
- Sponsoring Organization:
- (US)
- OSTI ID:
- 40203441
- Journal Information:
- Physical Review E, Vol. 63, Issue 6; Other Information: DOI: 10.1103/PhysRevE.63.066613; Othernumber: PLEEE8000063000006066613000001; 074106PRE; PBD: Jun 2001; ISSN 1063-651X
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
Similar Records
Spontaneous emission of radiation from a discrete sine-Gordon kink
Moving lattice kinks and pulses: An inverse method