{\phi}^4 Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics
Mathematical Physics
2018-05-02 v1 math.MP
Abstract
We explore a {\phi}^4 model with an added external parabolic potential term. This term dramatically alters the spectral properties of the system. We identify single and multiple kink solutions and examine their stability features; importantly, all of the stationary structures turn out to be unstable. We complement these with a dynamical study of the evolution of a single kink in the trap, as well as of the scattering of kink and anti-kink solutions of the model. We see that some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, are sensitively dependent on the trap strength parameter, as well as the initial displacement of the kink and antikink.
Keywords
Cite
@article{arxiv.1805.00206,
title = {{\phi}^4 Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics},
author = {R. M. Ross and P. G. Kevrekidis and D. K. Campbell and R. Decker and A. Demirkaya},
journal= {arXiv preprint arXiv:1805.00206},
year = {2018}
}