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Advances in Mathematical Physics
Volume 2014, Article ID 480670, 7 pages
Research Article

On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current

1School of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, China
2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China

Received 20 January 2014; Revised 25 March 2014; Accepted 27 March 2014; Published 14 April 2014

Academic Editor: Ricardo Weder

Copyright © 2014 Dali Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.