Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-29T12:49:31.062Z Has data issue: false hasContentIssue false

Similarity solutions of the generalized Korteweg–de Vries equation

Published online by Cambridge University Press:  01 September 1999

J. L. BONA
Affiliation:
Department of Mathematics and Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX 78712, USA
F. B. WEISSLER
Affiliation:
Laboratoire Analyse, Geométrie et Applications, UMA CNRS 7539, Institut Galilée-Université Paris XIII, F-93430, Villetaneuse, France

Abstract

Numerical simulations and group invariance considerations point to the existence of similarity solutions of the form

formula here

of the generalized Korteweg–de Vries equation

formula here

Here, x∗, t∗ and c are real parameters, x and t are real variables with tt∗, p is a positive integer and interest is focussed on the case where p[ges ]4 for which solutions of the initial-value problem for (**) are not known to be always globally defined. It is shown that smooth solutions of (**) of the form appearing in (*) do indeed exist. Some detailed properties of the function ψ appearing in (*) are also obtained.

Type
Research Article
Copyright
The Cambridge Philosophical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)