A System of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to the nonlinear Schr¨odinger equation (NLS) with a saturated nonlinearity. NLS 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 extending the work of [20], which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of [43]. Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.

• Type: Journal
• Year: 2010
• Where: JNS
• Authors: Jeremy L. Marzuola, Sarah Raynor, Gideon Simpson
• Keywords: Initial Data, JNS 2010, Minimal Mass Soliton, Soliton