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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 4 |
| Number of pages | 1 |
| Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 69 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2004 |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics