Damped and driven breathers and metastability

Caballero, Daniel; Wayne, C. Eugene

doi:10.1090/qam/1650

Authors: Daniel A. Caballero and C. Eugene Wayne
Journal: Quart. Appl. Math. 82 (2024), 7-33
MSC (2020): Primary 70H14, 37J25, 37J46
DOI: https://doi.org/10.1090/qam/1650
Published electronically: March 23, 2023
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Abstract: In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrödinger equations subject to spatially localized driving and damping. They provide an alternate description of the metastable behavior in such lattice systems which agrees with previous predictions for the evolution of metastable states while providing more accurate approximations to these states. We analyze the stability of these breathers, finding a very small positive eigenvalue whose eigenvector lies almost tangent to the surface of the cylinder formed by the family of breathers. This causes solutions to slide along the cylinder without leaving its neighborhood for very long times.

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