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 Painleve expansion, we then obtain an auto-Backlund 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.
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