复化的KdV方程的亚纯解结构

The meromophic solutions of the complex KdV equation

通过行波变换将KdV方程转变为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KdV方程w″+σ2w2-cw-b=0(其中σ,c,b为复常数)的亚纯解结构,且除了文章中所给的那些解外没有其它任何形式的亚纯解.

Through the traveling wave transformation in the paper, transform the KdV equation to the ordinary differential equation in complex field. Based on the knowledge of Nevanlinna valued distribution theory, investigate the forms of meromophic solutions of the complex KdV equation w″＋σ/2w^2-cw-b=0, where σ, c, b are complex constants, and there are no other meromophic solutions besides those explicit solutions found in this paper.