Phi-four solitary waves in a parabolic potentia: existence, stability, and collisional dynamics
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Citation (published version)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.
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.