Variational Approach to the Modulational Instability

Details Variational Approach to the Modulational Instability Variational Approach to the Modulational Instability

2004-04-25

arxiv.org/abs/cond-mat/0404601v1

Phys. Rev. E 69, 017601 (2004)

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1103/PhysRevE.69.017601

We study the modulational stability of the nonlinear Schr\"odinger 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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