2010/11/26 by Tetsu Mizumachi, Mizumachi, Tetsu, Dmitry Pelinovsky +1 · 1 citation
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.1011.5922
26 pages, no figures
arxiv created 2010/12/17 · arxiv updated 2010/12/20
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.