某些常微分方程的亚纯解表示与应用

本文运用Nevanlinna值分布理论研究了某些常微分方程亚纯解的存在性. 对于某些具有控制项的常系数常微分方程, 本文得到了亚纯解的表示, 并且给出了求相应偏微分方程精确解的一种方法.作为例子, 本文运用此方法得到了著名的KdV方程的所有亚纯行波精确解. 结果显示该方法比其他方法简单.

The representation of meromorphic solutions to certain ordinary differential equations and its applications

In this note, we employ the Nevanlinna''s value distribution theory to investigate the existence of meromorphic solutions to some complex ordinary differential equations. We obtain the representations of meromorphic solutions to complex ordinary differential equations with constant coefficients and dominant term, and give a new method to find the exact solutions to corresponding partial differential equations. As an example, we obtain all meromorphic traveling wave exact solutions to famous KdV equations by using the method. Our results show that the method is more simple than other methods.