New similarity solutions for the modified Boussinesq equation
- 7 July 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (13), 2355-2367
- https://doi.org/10.1088/0305-4470/22/13/029
Abstract
In this paper the author presents some new similarity solutions of the modified Boussinesq equation, which is a completely integrable soliton equation. These new similarity solutions include reductions to the second and fourth Painleve equations which are not obtainable using the standard Lie group method for finding group-invariant solutions of partial differential equations; they are determined using a new and direct method which involves no group theoretical techniques.Keywords
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