Similarity solutions of the Kadomtsev-Petviashvili equation
- 7 July 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (13) , L649-L654
- https://doi.org/10.1088/0305-4470/23/13/003
Abstract
Using the direct method introduced by Clarkson and Kruskal (CK) (1989) recently, the author obtains the similarity reductions of the Kadomtsev-Petviashvili equation (KPE). Some of them possess the same Painleve properties as that of the Boussinesq equation (BE) obtained by CK. However, the similarity solutions of KPE may include some (more than three) arbitrary functions of time. There exist some other types of similarity reductions of the KPE different from the similarity reductions of the BE obtained by CK.Keywords
This publication has 4 references indexed in Scilit:
- New similarity reductions of the Boussinesq equationJournal of Mathematical Physics, 1989
- Non-classical symmetry reduction: example of the Boussinesq equationJournal of Physics A: General Physics, 1989
- The relations among a special type of solutions in some (D+1)-dimensional nonlinear equationsJournal of Mathematical Physics, 1989
- Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebraJournal of Mathematical Physics, 1986