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Applications of KdV

In: KdV ’95

Author

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  • D. G. Crighton

    (University of Cambridge, Department of Applied Mathematics and Theoretical Physics)

Abstract

The discovery of the remarkable interaction properties of solitary wave solutions to KdV by Zabusky and Kruskal [62] and the invention by Gardner, Greene, Kruskal and Miura [9] of the Inverse Spectral Transform for the solution of the Cauchy problem for KdV stand as two of the most far-reaching breakthroughs in the development of modern nonlinear mathematical science. Of all the completely integrable systems discovered since 1967, KdV certainly remains the most fully understood and arguably the most important for applications to macroscopic phenomena and processes.

Suggested Citation

  • D. G. Crighton, 1995. "Applications of KdV," Springer Books, in: Michiel Hazewinkel & Hans W. Capel & Eduard M. de Jager (ed.), KdV ’95, pages 39-67, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-0017-5_2
    DOI: 10.1007/978-94-011-0017-5_2
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