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Nonlinear Sciences > Pattern Formation and Solitons

arXiv:nlin/0309031 (nlin)
[Submitted on 9 Sep 2003]

Title:Traveling solitons in the damped driven nonlinear Schrödinger equation

Authors:I.V. Barashenkov, E.V. Zemlyanaya
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Abstract: The well known effect of the linear damping on the moving nonlinear Schrödinger soliton (even when there is a supply of energy via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex traveling with zero momentum at a nonzero constant speed.
All traveling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to stabilize it.
Comments: 13 pages, 9 figures; to appear in SIAM Journal of Applied Mathematics
Subjects: Pattern Formation and Solitons (nlin.PS)
Report number: JINR preprint E17-2003-53
Cite as: arXiv:nlin/0309031 [nlin.PS]
  (or arXiv:nlin/0309031v1 [nlin.PS] for this version)
  https://doi.org/10.48550/arXiv.nlin/0309031

Submission history

From: Igor Barashenkov [view email]
[v1] Tue, 9 Sep 2003 12:44:36 UTC (50 KB)
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