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

Authors
Journal
Communications in Nonlinear Science and Numerical Simulation
1007-5704
Publisher
Elsevier
Publication Date
Volume
14
Issue
11
Identifiers
DOI: 10.1016/j.cnsns.2009.02.026
Keywords
  • The Second Painlevé Equation
  • Rational Solution
  • Bäcklund Transformation
  • (2 + 1)-Dimensional Nonlinear Evolution Equations
Disciplines
  • Mathematics

Abstract

Abstract 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.

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