Links between some (2+1)-dimensional nonlinear evolution equations and Painlevé-II equations

Using the idea of transformation, some links between (2+1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev–Petviashvili (KP) equation, generalized (2+1)-dimensional break soliton equation and (2+1)-dimensiona...

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Veröffentlicht in:Communications in nonlinear science & numerical simulation 2009-11, Vol.14 (11), p.3798-3803
Hauptverfasser: Jianqin, Mei, Dingjiang, Huang, Hongqing, Zhang
Format: Artikel
Sprache:eng
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Zusammenfassung:Using the idea of transformation, some links between (2+1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev–Petviashvili (KP) equation, generalized (2+1)-dimensional break soliton equation and (2+1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2+1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial Bäcklund transformations have been derived.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2009.02.026