The solitary waves,quasi-periodic waves and integrability of a generalized fifth-order Korteweg-de Vries equation |
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| Authors: | Pan-Li Ma Shou-Fu Tian Tian-Tian Zhang |
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| Institution: | 1. School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology , Xuzhou, People’s Republic of China.;2. Department of Mathematics, Hohai University Wentian College , Maanshan, People’s Republic of China. |
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| Abstract: | Under investigation in this paper is a fifth-order Korteweg-de Vries (fKdV) equation, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the binary Bell polynomials, a lucid and systematic approach is proposed to systematically study its bilinear representation, bilinear Bäcklund transformations and Lax pairs with explicit formulas, respectively. These results can be reduced to the ones of several integrable equations such as Sawada-Kotera equation, Caudrey-Dodd-Gibbon equation, Lax equation, Kaup-Kuperschmidt equation and Ito equation, etc. Furthermore, the N-solitary wave solutions formula and quasi-periodic wave solutions are obtained by using bilinear form of the fKdV equation. Finally, the relation between the periodic wave solution and solitary wave solution is rigorously established. |
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