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arXiv · 2108.00193

Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices

Faustino Palmero·Mario I. Molina·Jesús Cuevas-Maraver·Panayotis G. Kevrekidis
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Abstract

For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrodinger equation, where the linear operator of the Schrodinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.

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Faustino Palmero, Mario I. Molina, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis. 2021-07-31. Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices. https://doi.org/10.1016/j.physleta.2021.127880

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