This article focuses on two aspects. Firstly, symmetry analysis is performed for a nonlinear equation which can model surface wind wave patterns in nature. As a byproduct, the similarity reductions and exact solutions of the equation are constructed based on the optimal systems. Secondly, the explicit solutions are considered by the power series method. Moreover, the convergence of the power series solutions are shown.
Submitted July 21, 2016. Published August 23, 2016.
Math Subject Classifications: 35J05, 35E05, 43A80, 26A18.
Key Words: Nonlinear surface wind waves; symmetry analysis; similarity reduction; power series method.
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| Ben Gao |
College of Mathematics
Taiyuan University of Technology
Taiyuan 030024, China
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