Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation
Abstract
We study soliton solutions to a generalized Korteweg - de Vries (KdV) equation with a saturated nonlinearity, following the line of inquiry of the authors for the nonlinear Schr\"odinger equation (NLS). KdV with such a nonlinearity is known to possess a minimal-mass soliton. We consider a small perturbation of a minimal-mass soliton and identify a system of ODEs, which models the behavior of the perturbation for short times. This connects nicely to a work of Comech, Cuccagna & Pelinovsky (2007). These ODEs form a simple dynamical system with a single unstable hyperbolic fixed point with two possible dynamical outcomes. A particular feature of the dynamics are that they are non-oscillatory. This distinguishes the KdV problem from the analogous NLS one.
Keywords
Cite
@article{arxiv.1211.5677,
title = {Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation},
author = {Jeremy L. Marzuola and Sarah Raynor and Gideon Simpson},
journal= {arXiv preprint arXiv:1211.5677},
year = {2013}
}
Comments
17 pages, 8 figures