与WKI孤子族相应的完全可积的Bargmann系统

Completely Integrable Bargmann System Associated with the WKI Soliton Hierarchy

本文给出一个新的有限维对合系，并由此证明ＷＫＩ特征值问题在位势与谱函数之间的Ｂａｒｇｍａｎｎ约束下，被非线性化为一个Ｌｉｏｕｖｉｌｌｅ完全可积的Ｈａｍｉｌｔｏｎ系统，最后，我们由可换流的对合解获得ＷＫＩ方程族的每一方程解的表示．

A new finite-dimensional involutive system is presented,and theWKI hierarchy of nonlipear evolution equations and their commutator representationsare discussedin this article. By this finite-dimensional involutive system,it is proventhat under thd Bargmann constraints thc WKI eigenvalue problem is nonlinearized as acompletely integrable Hamiltonian system in the Liouville sense. Moreover,theinvolutive representation of solutions of each equation in the WKI hierarchy is obtainedby making use of the solution of two compatible system.