Variational Approach to the Modulational Instability
arXiv:cond-mat/0404601 · doi:10.1103/PhysRevE.69.017601
Abstract
We study the modulational stability of the nonlinear Schrödinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODEs, we re-derive the classical modulational instability criterion. The case (relevant to applications in optics and Bose-Einstein condensation) where the coefficients of the equation are time-dependent, is also examined.
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- Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review
- Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrodinger equation
- Stabilization of three-dimensional matter-waves solitons in an optical lattice
- Instability of Holographic Superfuids in Optical Lattice