Publication Date
2004
Abstract
We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE’s, we rederive 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.
Volume
69
Issue
1
Recommended Citation
Rapti, Z and Kevrekidis, PG, "Variational approach to the modulational instability" (2004). Mathematics and Statistics Department Faculty Publication Series. 1052.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1052
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v69/i1/e017601