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Z. Naturforsch. 67a, 132 – 140
(2012)
doi:10.5560/ZNA.2011-0071
Soliton Solutions, Bäcklund Transformation and Wronskian Solutions for the (2 + 1)-Dimensional Variable-Coefficient Konopelchenko–Dubrovsky Equations in Fluid Mechanics
1 Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
2 State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Received August 31, 2011 / published online April 2, 2012
Reprint requests to: Y.-T. G.; E-mail:
gaoyt@public.bta.net.cn
This paper is to investigate the (2 + 1)-dimensional variable-coefficient Konopelchenko–Dubrovsky equations, which can be applied to the phenomena in stratified shear flow, internal and shallow-water waves, plasmas, and other fields. The bilinear-form equations are transformed from the original equations, and soliton solutions are derived via symbolic computation. Soliton solutions and collisions are illustrated. The bilinear-form Bäcklund transformation and another soliton solution are obtained. Wronskian solutions are constructed via the Bäcklund transformation and solution.
Key words: (2 + 1)-Dimensional Variable-Coefficient Konopelchenko–Dubrovsky Equations; Fluid Mechanics; Soliton Solutions; Bäcklund Transformation; Wronskian Solutions; Symbolic Computation.
PACS numbers: 05.45.Yv; 47.35.Fg; 02.30.Jr; 02.30.Ik; 02.70.Wz