Rogue Wave Modes for the Long Wave--Short Wave Resonance Model

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概要

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• The long wave--short wave resonance model arises physically when the phase velocity of a long wave matches the group velocity of a short wave. It is a system of nonlinear evolution equations solvable by the Hirota bilinear method and also possesses a Lax pair formulation. ``Rogue wave'' modes, algebraically localized entities in both space and time, are constructed from the breathers by a singular limit involving a ``coalescence'' of wavenumbers in the long wave regime. In contrast with the extensively studied nonlinear Schrödinger case, the frequency of the breather cannot be real and must satisfy a cubic equation with complex coefficients. The same limiting procedure applied to the finite wavenumber regime will yield mixed exponential-algebraic solitary waves, similar to the classical ``double pole'' solutions of other evolution systems.

• 2013-07-15

著者

• Grimshaw Roger

  Department Of Mathematical Sciences Loughborough University

• Chow Kwok

  Department Of Mathematics University Of Arizona

• Chan Hiu

  Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong

• Kedziora David

  Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia

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• Rogue Wave Modes for the Long Wave--Short Wave Resonance Model
• Rogue Wave Modes for the Long Wave–Short Wave Resonance Model

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