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Similarity solutions of the generalized Korteweg–de Vries equation
Published online by Cambridge University Press: 01 September 1999
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 t≠t∗, 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
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 2 , September 1999 , pp. 323 - 351
- Copyright
- The Cambridge Philosophical Society 1999
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