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Zbl 0698.35137
Clarkson, Peter A.; Kruskal, Martin D.
New similarity reductions of the Boussinesq equation. (English)
[J] J. Math. Phys. 30, No.10, 2201-2213 (1989). ISSN 0022-2488; ISSN 1089-7658/e

Summary: Some new similarity reductions of the Boussinesq equation, which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering, are presented. These new similarity reductions, including some new reductions to the first, second, and fourth Painlevé equations, cannot be obtained using the standard Lie group method for finding group-invariant solutions of partial differential equations; they are determined using a new and direct method that involves no group theoretical techniques.

MSC 2000:: *35Q99 PDE of mathematical physics and other areas
58J72 Correspondences and other transformation methods
37J35 Completely integrable systems, etc.
37K10 Completely integrable systems etc.

Keywords: Boussinesq equation; similarity reductions; Painlevé equations

Cited in: Zbl 1183.35238 Zbl 1170.76049 Zbl 1141.35455 Zbl 1202.37106 Zbl 0990.35104 Zbl 1003.76019 Zbl 0958.35015 Zbl 1020.35083 Zbl 0830.35120 Zbl 0819.35125 Zbl 0822.35005 Zbl 0797.35149 Zbl 0788.35067 Zbl 0772.35065 Zbl 0764.35100 Zbl 0771.35053 Zbl 0754.35148 Zbl 0752.35064 Zbl 0734.35123 Zbl 0734.35122

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