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Kink dynamics in a parametric $\phi^6$ system: a model with controllably many internal modes

Banff International Research Station for Mathematical Innovation and Discovery

In the present work, we intend to explore a variant of the $\phi^6$ model originally proposed in \textit{Phys. Rev. D} \textbf{12}, 1606 (1975) as a prototypical, so-called, ``bag'' model where domain walls play the role of quarks within hadrons. We examine the prototypical steady state of the model, namely an apparent bound state of two kink structures. We explore its linearization and find that as a function of a prototypical parameter controlling the curvature of the potential an effectively arbitrary number of internal modes may arise in the point spectrum of the linearized analysis. We \textit{intend to} use Evans function analysis to predict the bifurcation points of the relevant internal modes and confirm these theoretical predictions numerically. Finally, given the remarkable flexibility of the model in possessing different numbers of internal modes we \textit{once again intend to} explore the dynamics of multi-bound-state collisions to identify the role of the additional internal modes in enhancing the complexity of the observed scattering scenarios. I. Christov, P. G. Kevrekidis, A. Saxena, and R. Decker are my collaborators.

Mathematics; Partial differential equations; Dynamical systems and ergodic theory; Functional analysis

video/mp4

Author affiliation: University of Hartford

2017-12-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64108

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/