Phi-four solitary waves in a parabolic potentia: existence, stability, and collisional dynamics
Files
Accepted manuscript
Date
2019-09
DOI
Authors
Campbell, David K.
Ross, R.M.
Kevrekidis, P.G.
Decker, R.
Demirkaya, A.
Version
Accepted manuscript
OA Version
Citation
David Campbell, R.M. Ross, P.G. Kevrekidis, R. Decker, A. Demirkaya. 2019. "Phi-four solitary waves in a parabolic potentia: existence, stability, and collisional dynamics." Springer Series Nonlinear Systems and Complexity, Volume 26, pp. 213 - 234.
Abstract
We explore a φ4 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 observe 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.