Bäcklund Transformations,Solitary Waves,Conoid Waves and Bessel Waves of the (2+1)-Dimensional Euler equation |
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| Authors: | Sen Yue Lou Man Jia Fei Huang Xiao Yan Tang |
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| Institution: | (1) Center of Nonlinear Science, Ningbo University, Ningbo, 315211, China;(2) Department of Physics, Shanghai Jiao Tong University, Shanghai, 200030, China;(3) Department of Physics, North China Coal Medical College, Tangshan, 063000, China;(4) Department of Marine Meteorology, Ocean University of China, Qingdao, 266003, China;(5) Department of Physics, Shanghai Jiao Tong University, Shanghai, 200030, China |
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| Abstract: | Some simple special Bäcklund transformation theorems are proposed and utilized to obtain exact solutions for the (2+1)-dimensional Euler equation. It is found that the (2+1)-dimensional Euler equation possesses abundant soliton or solitary wave structures, conoid periodic wave structures and the quasi-periodic Bessel wave structures on account of the arbitrary functions in its solutions. Moreover, all solutions of the arbitrary two dimensional nonlinear Poisson equation can be used to construct exact solutions of the (2+1)-dimensional Euler equation. |
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| Keywords: | B?cklund transformations theorems (2+1)-dimensional Euler equation Solitary waves Conoid periodic wave Bessel wave |
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