一族Liouville可积系及其Hamilton结构

A family of Liouville integrable system and its Hamiltonian structure

指出了获得可积系的方法一般是在零曲率框架Ut-V(n)x+[U,V(n)]=0中进行,所选取的V的形式为V=∑m≥0Vmλ-m,Vm=ambmcm-am.构造了一个等谱问题,特别是对于该等谱问题,选取的V中既含有谱位势,又含有a,b,c的关于x的导数项,得到了一个新的Lax对.利用屠格式获得了一族新的Liouville可积系,具有Hamil ton结构.

A general method for obtaining integrable systems is implemented in the frame of zerocurvature equation Ut-V(n)x+=0, where V is chosen to be of the form V=∑m≥0Vmλ-m,Vm=ambm cm-am. An isospectral problem is first constructed in this paper. In particular, for the given spectral problem, the chosen V contains spectral potentials as well as derivatives of a,b,c with respect to x, which are to be determined, so that a new Lax pair is resulted. Then, using Tumodel, a family of new Liouville integrable system with Hamiltonian structure is obtained.