Stability of cnoidal waves in the parametrically driven nonlinear Schr\"odinger equation
Pattern Formation and Solitons
2012-01-04 v1
Abstract
The parametrically driven, damped nonlinear Schr\"odinger equation has two cn- and two dn-wave solutions. We show that one pair of the cn and dn solutions is unstable for any combination of the driver's strength, dissipation coefficient and spatial period of the wave; this instability is against periodic perturbations. The second dn-wave solution is shown to be unstable against antiperiodic perturbations --- in a certain region of the parameter space. We also consider quasiperiodic perturbations with long modulation wavelength, in the limit where the driving strength is only weakly exceeding the damping coefficient.
Cite
@article{arxiv.1201.0263,
title = {Stability of cnoidal waves in the parametrically driven nonlinear Schr\"odinger equation},
author = {I. V. Barashenkov and M. A. Molchan},
journal= {arXiv preprint arXiv:1201.0263},
year = {2012}
}
Comments
14 pages, 6 figures