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arXiv · 1211.5677

Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation

Jeremy L. Marzuola·Sarah Raynor·Gideon Simpson
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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 Schrödinger 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.

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Jeremy L. Marzuola, Sarah Raynor, Gideon Simpson. 2013-01-22. Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation. https://arxiv.org/abs/1211.5677

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