(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

Article

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.

Keywords

Surface Tension Exact Solution Wave Propagation Surface Wave Solitary Wave 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.State Key Laboratory of Software Development EnvironmentBeijing University of Aeronautics and AstronauticsBeijingChina
  3. 3.CCAST (World Lab.)BeijingChina
  4. 4.Ministry of Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid DynamicsBeijing University of Aeronautics and AstronauticsBeijingChina

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