Eur. Phys. J. B 42, 441-450 (2004)
https://doi.org/10.1140/epjb/e2004-00402-8

(2+1) dimensional Hărăgus-Courcelle-Il'ichev model for the liquid surface waves in the presence of sea ice or surface tension: Bäcklund transformation, exact solutions and possibly observable effects

¹ School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China
² State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
³ CCAST (World Lab.), P.O. Box 8730, Beijing 100080, China
⁴ Ministry of Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China (Mailing address for YTG)

Corresponding author: ^a gaoyt@public.bta.net.cn

Received: 21 July 2004
Published online: 23 December 2004

Abstract

The wave propagation on an ocean or water surface in the presence of sea ice or surface tension is of current importance. In this paper, we investigate the (2+1) dimensional 6th-order model proposed recently by Hărăgus-Courcelle and Il'ichev for such wave propagation. Firstly, we correct some errors in the original derivations of this model. With computerized symbolic computation and truncated Painlevé expansion, we then obtain an auto-Bäcklund transformation and types of the solitonic and other exact analytic solutions to the model, with the solitary waves as a special case, able to be dealt with the powerful Wu method. Based on the results, we later propose some possibly observable effects for the future experiments, and in the end, provide a possible way to explain the regular structure of the open-sea ice break-up observations.