✦ LIBER ✦

Rational solutions of fifth-order evolutionary equations for describing waves on water

✍ Scribed by Yu.Yu. Bagderina

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 499 KB
Volume: 72
Category: Article
ISSN: 0021-8928
DOI: 10.1016/j.jappmathmech.2008.04.006

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✦ Synopsis

A method is proposed for obtaining the exact solutions of evolutionary equations in the form of a rational function. Invariant manifolds of the equations are used which have the same form of dependence on the required function and its derivatives as the generalized Riccati equations. Using fifth-order Kawahara and Korteweg-de Vries equations as an example, it is shown that their known particular solutions can be obtained using this method. New solutions of a non-linear fifth-order equation, which is encountered when describing long waves on water, are obtained.

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