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The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

Published online by Cambridge University Press:  29 March 2006

Harvey Segur
Harvey Segur
Affiliation:
Mathematics Department, Clarkson College of Technology, Potsdam, N.Y.
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Abstract

The method of solution of the Korteweg–de Vries equation outlined by Gardner et al. (1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 4 , 7 August 1973 , pp. 721 - 736
Copyright
© 1973 Cambridge University Press

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