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Nonlinear dispersion relations

Author

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  • Ludu, A.
  • Kevrekidis, P.G.

Abstract

We examine how nonlinear dispersion relations (NLDR) can be used as a simple, universal algebraic tool to provide information for the localized, nonlinear solutions of PDE that model physical systems. Such scaling relations between width, amplitude and velocity are of great help for numerical investigations of nonlinear solutions. The methodology is applied to a variety of examples from diverse branches of physics, both Hamiltonian as well as dissipative ones. The limitations of the approach are also discussed.

Suggested Citation

  • Ludu, A. & Kevrekidis, P.G., 2007. "Nonlinear dispersion relations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(2), pages 229-236.
    • Handle: RePEc:eee:matcom:v:74:y:2007:i:2:p:229-236
    DOI: 10.1016/j.matcom.2006.10.003
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    Cited by:

    1. Ilison, Lauri & Salupere, Andrus, 2009. "Propagation of sech2-type solitary waves in hierarchical KdV-type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3314-3327.
    2. Yin, Jiuli & Tian, Lixin, 2009. "Stumpons and fractal-like wave solutions to the Dullin–Gottwald–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 643-648.

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