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Modulational instabilities in the discrete deformable nonlinear Schrödinger equation

Yuri S. Kivshar, Mario Salerno

Abstract

We study analytically and numerically modulational instability for the discrete deformable nonlinear Schr\"odinger (NLS) equation which represents a natural link between the properties of the integrable Ablowitz-Ladik model and the nonintegrable discrete NLS equation. We show how different discretizations of the nonlinear interaction change modulational instability in the lattice and, correspondingly, conditions for localized modes to exist.

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Key concepts: Modulational instability, Integrable system, Physics, Nonlinear Schrödinger equation, Nonlinear system, Instability, Classical mechanics, Lattice (music)