The Meromorphic Solutions of the Complex Higher order KdV Equation
BAI Lingling1, WU Qifeng2, YUAN Wenjun3
1. School of Basic Sciences, Shanghai Aurora Vocational College, Shanghai 201908;2. Shaozhou Normal College, Shaoguan University, Shaoguan 512009;3. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006
Using the travelling wave transformation in the paper,transform the higher order KdV equation to the ordinary differential equation in the complex field. Based on the knowledge of Nevanlinna valued-distribution theory , investigate the forms of meromorphic solutions of the complex higher order KdV equation w(4)+w''+(1/2)w2-cw-b=0, where c,b are complex constants,and obtain that there are no other meromorphic solutions besides those three class explicit solutions found in this paper. For two class higher order (nKdV)1 and (mKdV)2, it is not determinant that there are the similar solutions of the corresponding ordinary differential equation in the complex plane if n=2,3 and m=3. For (2KdV)2, there are possible four class explicit meromorphic solutions.