Abstract
This paper is concerned with the variable-coefficient Gardner (vc-Gardner) types of equations, which arise in fluid dynamics, nonlinear lattice and plasma physics. As its special cases, the generalized cylindrical KdV types of equations are considered simultaneously. By using the combination of Painlevé analysis and Lie group classification method, the integrable conditions, Bäcklund transformations and complete group classifications of the vc-Gardner types of equations are obtained. Then, the exact solutions generated from the Painlevé analysis and symmetry reductions are investigated.
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The authors are grateful to the editors and anonymous reviewers for their valuable comments and suggestions.
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This work is supported by the National Natural Science Foundation of China under Grant No. 11171041 and the doctorial foundation of Liaocheng University under Grant No. 31805.
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Liu, H., Li, J. Painlevé analysis, complete Lie group classifications and exact solutions to the time-dependent coefficients Gardner types of equations. Nonlinear Dyn 80, 515–527 (2015). https://doi.org/10.1007/s11071-014-1885-0
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DOI: https://doi.org/10.1007/s11071-014-1885-0
Keywords
- Painlevé analysis
- Integrable condition
- Bäcklund transformation
- Complete group classification
- Symmetry reduction
- Exact solution