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《Journal of Jiangxi Normal University(Natural Science Edition)》 2017-06
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The Traveling Wave Meromorphic Solutions of a Kind of Complex Higher-Order KdV Equations

YUAN Wenjun;DANG Guoqiang;School of Mathematics and Information Science,Guangzhou University;  
In this paper,a class of fifth-order KdV equations u_t+ δu~2u_x+ βu_xu_(xx)+ γuu_(xxx)+ ωu_(xxxxx)= 0 are considered. These KdV equations are reduced as a class of complex ordinary differential equations w( 4)+ δww″ +βw'2+ γw3+ λw + μ = 0,by using the traveling wave transformation u( x,t) = w( z),z = x + λt( λ ≠ 0),whose dominant parts have four terms E( z,w) = w( 4)+ δww″ + βw'2+ γw3. The main result is that the meromorphic solutions of the equations are obtained as elliptic function solutions,rational function solutions,and rational function solutions of e~(αz)( α ∈ C),by employing complex method. Furthermore,two examples u_t+ u_(xxxxx)+ 5 uu_(xxx)+15u_xu_(xx)+5u~2u_x= 0( modified Sawada-Kotera equation) and u_t-u_(xxxxx)+ 20 uu_(xxx)+ 50 u_xu_(xx)-80 u~2u_x= 0( KaupKupershmid equation) are given to show that besides the meromorphic solutions which are confirmed,some equations maybe have other meromorphic solutions.
【Fund】: 国家自然科学基金(11271090);; 广东省自然科学基金(2016A030310257 2015A030313346)资助项目
【CateGory Index】: O174.52;O175
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