非线性偏微分方程之间的Miura变换

The Miura transformation between nonlinear partial differential equations

为了找出uxxx=p(u)+q(u)ux+ut之间新的Miura变换,推出了uxxx=p(u)+q(u)ux+ut的可积系统,导出了方程之间的Miura变换,并举例运用Miura变换,由方程的已知解u求出另一方程的解φ,同时由方程的已知Backlund变换求出另一方程的Backlund变换.

A new integrable system associated withuxxx=p（u）＋q（u）ux ＋ ut was obtained for looking for a new Miura transformation from nonlinear partial differential equationuxxx=p（u）＋q（u）ux ＋ u t to other nonlinear partial differential equation.The Miura transformation was found,for some examples,by applying Miura transformation,solutionφ from known solutionu and a Backlund transformation for a nonlinear partial differential equation was gained.