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Three-dimensional Korteweg-de Vries equation and traveling wave solutions

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  • Kenneth L. Jones

Abstract

The three-dimensional power Korteweg-de Vries equation [ u t + u n u x + u x x x ] x + u y y + u z z = 0 , is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n = 1 and n = 2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.

Suggested Citation

  • Kenneth L. Jones, 2000. "Three-dimensional Korteweg-de Vries equation and traveling wave solutions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:712798
    DOI: 10.1155/S0161171200004440
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