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.
出处
《应用数学学报》
CSCD
北大核心
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
