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Nonlinear Sciences > Pattern Formation and Solitons

arXiv:nlin/0302041 (nlin)
[Submitted on 17 Feb 2003]

Title:Instabilities in the two-dimensional cubic nonlinear Schrodinger equation

Authors:John D. Carter, Harvey Segur
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Abstract: The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional traveling wave solution of NLS with trivial phase is unstable with respect to some infinitesimal perturbation with two-dimensional structure. If the coefficients of the linear dispersion terms have the same sign then the only unstable perturbations have transverse wavelength longer than a well-defined cut-off. If the coefficients of the linear dispersion terms have opposite signs, then there is no such cut-off and as the wavelength decreases, the maximum growth rate approaches a well-defined limit.
Comments: 4 pages, 4 figures
Subjects: Pattern Formation and Solitons (nlin.PS)
Cite as: arXiv:nlin/0302041 [nlin.PS]
  (or arXiv:nlin/0302041v1 [nlin.PS] for this version)
  https://doi.org/10.48550/arXiv.nlin/0302041
Related DOI: https://doi.org/10.1103/PhysRevE.68.045601

Submission history

From: John Carter [view email]
[v1] Mon, 17 Feb 2003 19:26:48 UTC (21 KB)
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