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INTEGRABLE PROPERTIES AND SIMILARITY REDUCTIONS OF THE SINE-LAPLACE EQUATION FROM AN INVISCID INCOMPRESSIBLE FLUID WITH SYMBOLIC COMPUTATION

School of Science, P. O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China

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GUANG-MEI WEI

Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

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HAI-QIANG ZHANG

School of Science, P. O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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https://doi.org/10.1142/S0217979210053628Cited by:0 (Source: Crossref)

Abstract

Several integrable properties of the Sine-Laplace equation arising from an inviscid incompressible fluid are symbolically presented, including the Lax pair, auto-Bäcklund transformation, nonlinear superposition formula, bilinear form, and static N-soliton solution. Furthermore, with symbolic computation, two similarity reductions for the Sine-Laplace equation are derived by virtue of the classical Lie group method of infinitesimal transformations. One reduces to the third Painlevé equation and the other to a known ordinary differential equation. Sample static solutions are discussed and pictured.

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