高阶KdV方程的复化解结构  

The Meromorphic Solutions of the Complex Higher order KdV Equation

作　　者：柏玲玲[1] 吴奇峰[2] 袁文俊[3] 

机构地区：[1]上海震旦职业学院基础部,上海201908 [2]韶关学院韶州师范分院,韶关512009 [3]广州大学数学与信息科学学院,广州510006

出　　处：《应用数学学报》2010年第4期681-689,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10771220);国家教育部博士点基金(200810780002)资助项目

摘　　要：通过行波变换将高阶KdV方程转换成复域中的常微分方程,以Nevanlinna值分布理论的有关知识为基础,研究了复化的高阶KdV方程w^((4))+w″+1/2w^2-cw-b=0(其中c,b为复常数)的亚纯解结构,确定了可能的三种形式的亚纯解.对于两类高阶方程(_nKdV)_1和(_mKdV)_2,当n=2,3和m=3时,不能确定相应的复化方程有类似亚纯解结构;当m=2时,相应复化方程具有具体形式的亚纯解.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 equationω^（（4）） ＋ω″＋（1/2）ω^2-cω-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.

关 键 词：KDV方程 亚纯函数 椭圆函数 NEVANLINNA理论 

分 类 号：O175.4[理学—数学]