一个能量与位势相依的二阶谱问题及其相关的发展方程族

The Second-order Spectral Problem of Energy Depended on Potential and Hierarchy of Evolution Equations

本文将研究一个二阶谱系及相关的非线性发展方程及其Hamilton系统,利用Lax对非线性化方法,讨论经典力学的Jacobi-Ostrogradsky坐标,得到Bargmann约束下完全可积的Hamilton系统,通过Bargmann约束,从而给出发展方程族解的对合表示。

In this paper, the nonlinear evolution equation and the Hamilton system related to a sec- ond-order spectral problem are studied. Using the nonlinearization approach of Lax pairs, the Jacobi-Os- trogradsky coordinates of classical mechanics is discussed. Finally the completely integrable Hamilton system can be obtained in the Bargmann constraint condition, and the involutive solutions of the evolu- tion equations are given.