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Non Classical Solitary Waves

In: Differential Equations Theory, Numerics and Applications

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  • Jean Claude Saut

    (Analyse Numérique et EDP CNRS et Université Paris Sud)

Abstract

This lecture will survey some recent results, mainly due to Anne de Bouard and the author, on solitary waves solutions to nonlinear dispersive equations with weak transverse effects. Typical examples are the generalized Kadomtsev Petviashvili equation or the equation for Langmuir waves in a weakly magnetized plasma. Those solitary waves are not “classical” in the sense that (contrarily to the solitary waves of the Korteweg de Vries or the usual nonlinear Schrödinger equations), they are not radial and do not decay rapidly at infinity. This is due to the breaking of radial symmetry which leads to the anisotropy of the underlying partial differential equation.

Suggested Citation

  • Jean Claude Saut, 1997. "Non Classical Solitary Waves," Springer Books, in: E. van Groesen & E. Soewono (ed.), Differential Equations Theory, Numerics and Applications, pages 125-137, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5157-3_6
    DOI: 10.1007/978-94-011-5157-3_6
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