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A System of ODEs for a Perturbation of a Minimal Mass Soliton
Journal article   Open access   Peer reviewed

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

Jeremy L. Marzuola, Sarah Raynor and Gideon Simpson
Journal of nonlinear science, v 20(4), pp 425-461
01 Aug 2010
DOI: https://doi.org/10.1007/s00332-010-9064-z
url
http://arxiv.org/abs/0905.0513View
SubmittedOpen Access (License Unspecified),  Open

Abstract

Mathematics Mathematics, Applied Mechanics Physical Sciences Physics Physics, Mathematical Science & Technology Technology
We study soliton solutions to the nonlinear Schrodinger 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 Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), 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 Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). 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.

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Domestic collaboration
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Mathematics, Applied
Mechanics
Physics, Mathematical
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