In this paper,the governing equation for the non-propagating solitary waves,similar to the cubicSchr(?)dinger equation,is derived by the multiple scales with the consideration of surface tension.The non-propagatingsol...In this paper,the governing equation for the non-propagating solitary waves,similar to the cubicSchr(?)dinger equation,is derived by the multiple scales with the consideration of surface tension.The non-propagatingsolitary wave solution is given.It is explained by the capillary-gravity wave theory that the crests are sharpened and thetroughs are flattened in the transversal harmonic of the non-propagating solitary waves.On σ～kh plane,twoparameter regions are obtained in which the non-propagating solitary wave can occur,but all existing experimentalparameters are in region 1(Fig.1).展开更多
Using the mapping method based on q-deformed hyperbolic functions,the exact solutions of generalizedBreor-Kaup equations are obtained.Based on the solutions,two coherent structures,periodic-branch kink and non-propaga...Using the mapping method based on q-deformed hyperbolic functions,the exact solutions of generalizedBreor-Kaup equations are obtained.Based on the solutions,two coherent structures,periodic-branch kink and non-propagating kink,have been obtained.Moreover,one solitonal interaction form,two line solitons interaction on the kinkbackground,has been found.展开更多
文摘In this paper,the governing equation for the non-propagating solitary waves,similar to the cubicSchr(?)dinger equation,is derived by the multiple scales with the consideration of surface tension.The non-propagatingsolitary wave solution is given.It is explained by the capillary-gravity wave theory that the crests are sharpened and thetroughs are flattened in the transversal harmonic of the non-propagating solitary waves.On σ～kh plane,twoparameter regions are obtained in which the non-propagating solitary wave can occur,but all existing experimentalparameters are in region 1(Fig.1).
基金National Natural Science Foundation of China under Grant Nos.10535010 and 10775123the Research Fund of Ministry of Education under Grant No.20070284016
文摘Using the mapping method based on q-deformed hyperbolic functions,the exact solutions of generalizedBreor-Kaup equations are obtained.Based on the solutions,two coherent structures,periodic-branch kink and non-propagating kink,have been obtained.Moreover,one solitonal interaction form,two line solitons interaction on the kinkbackground,has been found.
