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Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0203007 (nlin)
[Submitted on 5 Mar 2002 (v1), last revised 29 Jan 2003 (this version, v2)]

Title:Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary pde

Authors:Darryl D. Holm, Martin F. Staley
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Abstract: We study exchange of stability in the dynamics of solitary wave solutions under changes in the nonlinear balance in a 1+1 evolutionary partial differential equation related both to shallow water waves and to turbulence. We find that solutions of the equation $ m_t + um_x +b u_xm = \nu m_{xx} $ with $m = u - \alpha^2 u_{xx}$ for fluid velocity $u(x,t)$ change their behavior at the special values $b=0,\pm1,\pm2,\pm3$.
Comments: 15 pages, 8 figures. For this replacement of the original submission, we: (1) Introduced key explanations that clarify the differences between Figs 1 and 2, versus 3 and 4. (2) Expanded the introduction to provide added motivation and precise definitions. (3) Added section and subsection headings to make the plan of the paper more evident. (4) Added a brief summary
Subjects: Chaotic Dynamics (nlin.CD); Pattern Formation and Solitons (nlin.PS)
Cite as: arXiv:nlin/0203007 [nlin.CD]
  (or arXiv:nlin/0203007v2 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0203007
Related DOI: https://doi.org/10.1016/S0375-9601%2803%2900114-2

Submission history

From: Martin Staley [view email]
[v1] Tue, 5 Mar 2002 23:57:15 UTC (616 KB)
[v2] Wed, 29 Jan 2003 21:49:29 UTC (627 KB)
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