Stability of Discrete Solitons in the Presence of Parametric Driving

Abstract

In this brief report, we consider parametrically driven bright solitons in the vicinity of the anti-continuum limit. We illustrate the mechanism through which these solitons become unstable due to the collision of the phase mode with the continuous spectrum, or eigenvelues bifurcating thereof. We show how this mechanism typically leads to complete destruction of the bright solitary wave.

4 pages, 4 figures

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• Dissipative structures in a parametrically driven dissipative lattice: chimera, localized disorder, continuous-wave, and staggered state
• Bifurcation Results for Traveling Waves in Nonlinear Magnetic Metamaterials
• Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons
• Solitons in a parametrically driven damped discrete nonlinear Schrödinger equation