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The Korteweg—de Vries Equation and Beyond

In: KdV ’95

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  • A. S. Fokas

    (Clarkson University, Department of Mathematics and Computer Science and Institute for Nonlinear Studies)

Abstract

We review a new method for linearizing the initial-boundary value problem of the KdV on the semi-infinite line for decaying initial and boundary data. We also present a novel class of physically important integrable equations. These equations, which include generalizations of the KdV, of the modified KdV, of the nonlinear Schrödinger and of the N-wave interactions, are as generic as their celebrated counterparts and, furthermore it appears that they describe certain physical situations more accurately.

Suggested Citation

  • A. S. Fokas, 1995. "The Korteweg—de Vries Equation and Beyond," Springer Books, in: Michiel Hazewinkel & Hans W. Capel & Eduard M. de Jager (ed.), KdV ’95, pages 295-305, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-0017-5_15
    DOI: 10.1007/978-94-011-0017-5_15
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