Variational approach to the modulational instability

Year: 2004

Authors: Rapti Z., Kevrekidis P.G., Smerzi A., Bishop A.R.

Autors Affiliation: Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA; Univ Trent, Ist Nazl Fis Mat, BEC, CRS, I-38050 Trento, Italy; Univ Trent, Dipartimento Fis, I-38050 Trento, Italy; Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA; Los Alamos Natl Lab, Ctr Nonlinear Studies, Los Alamos, NM 87545 USA.

Abstract: We study the modulational stability of the nonlinear Schrodinger 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.

Journal/Review: PHYSICAL REVIEW E

Volume: 69 (1)      Pages from: 17601-1  to: 17601-4

KeyWords: Quantum-theory; Optical-fibers; Dynamics; Solitons; Waves; Field
DOI: 10.1103/PhysRevE.69.017601

Citations: 36
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