考虑一类常微分方程Aw″+Bw′+Cw+Dw2+E=0, 然后运用一个新方法——复方法, 得出此类辅助常微分方程的亚纯函数通解,并运用这些结果得到Fisher方程、Oskolkov方程、BBMPB方程和OBBMB方程的所有亚纯行波精确解.结果显示,Fisher方程、Oskolkov方程、BBMPB方程和OBBMB方程的所有单周期函数解为孤立行波解,而且复方法比其他方法更简捷有效.
Abstract
In this paper, we consider a class of ordinary differential equation Aw″+Bw′+Cw+Dw2+E=0, and then we use a new method named complex method to derive the general meromorphic solutions for this auxiliary ordinary differential equation. At last, all traveling wave exact solutions for the Fisher equation, Oskolkov equation, BBMPB equantion and OBBMB equation can be found by our results. Our results shows that all simple periodic exact solutions in the Fisher equation, Oskolkov equation, BBMPB equantion and OBBMB equation are solitary wave solutions, and the complex method is simpler and more precise than other methods.
关键词
微分方程 /
通解 /
亚纯函数 /
椭圆函数
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Key words
differential equation /
general solution /
meromorphic function /
elliptic function
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参考文献
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