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Stability of traveling waves in a nonlinear hyperbolic system approximating a dimer array of oscillators
Huaiyu Li, Andrew Hofstrand, Michael I. Weinstein
https://arxiv.org/abs/2402.07567

Stability of traveling waves in a nonlinear hyperbolic system approximating a dimer array of oscillators
We study a semilinear hyperbolic system of PDEs which arises as a continuum approximation of the discrete nonlinear dimer array model introduced by Hadad, Vitelli and Alu (HVA) in \cite{HVA17}. We classify the system's traveling waves, and study their stability properties. We focus on traveling pulse solutions (``solitons'') on a nontrivial background and moving domain wall solutions (kinks); both arise as heteroclinic connections between spatially uniform equilibrium of a reduced dynamical sys…