一个三阶非线性发展方程的双Hamilton结构

Bi-Hamiltonian Structure of a 3^(rd) Order Non-linear Evolution Equation

研究了三阶非线性发展方程:ut=12((uxx+u)-2)x在M iura变换下的方程:vt=12(-v 2)xxx+12(v-2)x,得到了后一个方程的遗传算子,并且利用该算子的D-ε1型分解,证明了此方程是一个双H am ilton系统.

A 3rd order non-linear evolution equation Vt=1/2（v^-2）xxx＋1/2（v^-2）x derived from equation ut=1/2（（uxx＋u）^-2x by a Miura transformation is studied. A hereditary operator eorresponding to the equation is obtained. Moreover, the bi-Hamiltonian structure of the equation are found by using decomposition of the hereditary operator of form Dε^-1.