Instability of double-periodic waves in the nonlinear Schrodinger equation
Abstract
It is shown how to compute the instability rates for the double-periodic solutions to the cubic NLS (nonlinear Schrodinger) equation by using the Lax linear equations. The wave function modulus of the double-periodic solutions is periodic both in space and time coordinates; such solutions generalize the standing waves which have the time-independent and space-periodic wave function modulus. Similar to other waves in the NLS equation, the double-periodic solutions are spectrally unstable and this instability is related to the bands of the Lax spectrum outside the imaginary axis. A simple numerical method is used to compute the unstable spectrum and to compare the instability rates of the double-periodic solutions with those of the standing periodic waves.
Keywords
Cite
@article{arxiv.2012.15344,
title = {Instability of double-periodic waves in the nonlinear Schrodinger equation},
author = {Dmitry E. Pelinovsky},
journal= {arXiv preprint arXiv:2012.15344},
year = {2021}
}
Comments
15 pages, 7 figures