Backlund transformation and L2-stability of NLS solitons
Exactly Solvable and Integrable Systems
2010-12-20 v2 Pattern Formation and Solitons
Abstract
Ground states of a L2-subcritical focusing nonlinear Schrodinger (NLS) equation are known to be orbitally stable in the energy class H1 thanks to its variational characterization. In this paper, we will show L2-orbital stability of 1-solitons to a one-dimensional cubic NLS equation for any initial data which are close to 1-solitons in L2. Moreover, we prove that if the initial data are in H3 in addition to being small in L2, then the solution remains in an L2-neighborhood of a specific 1-soliton solution for all the time. The proof relies on the Backlund transformation between zero and soliton solutions of this integrable equation.
Keywords
Cite
@article{arxiv.1011.5922,
title = {Backlund transformation and L2-stability of NLS solitons},
author = {Tetsu Mizumachi and Dmitry Pelinovsky},
journal= {arXiv preprint arXiv:1011.5922},
year = {2010}
}
Comments
26 pages, no figures