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arXiv · 1805.00206

{\phi}^4 Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics

R. M. Ross·P. G. Kevrekidis·D. K. Campbell·R. Decker·A. Demirkaya
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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.

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R. M. Ross, P. G. Kevrekidis, D. K. Campbell, R. Decker, A. Demirkaya. 2018-05-01. {\phi}^4 Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics. https://arxiv.org/abs/1805.00206

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