一族非线性发展方程解的对合表示及所对应的对合守恒积分系

The Involutive Representation of Solutions of a Hierarchy of Nonlinear Evolution Equations and Their Corresponding Involutive Systems of Conserved Integrals

本文针对线性谱问题利用“非线性化”方法给出与之相应的一族非线性发展方程解的对合表示；并证明了文献［１］中节４中４）里的对合守恒积分系Ｆ＿ｍ：实际上是由该族方程Ｌａｘ表示的时间部分之非线性化而导致；另外，顺便还给出了一个驻定的非线性系统．

For the linear spectral problem:by the method of so-called“nonlinearization”,the involutive representation of solutions of a hierarchy of nonlinear evolution equations associated with(*)is presented in this paper. It is proved that the involutive systems of conserved inte-grals F_m in 4)of section 4 in ref.[1]is actually produced by the nonlinearization of the time part of the Lax representa-tion for this hierarchy of equations.The involutity of F_m is shown by a simplermethod and a stationary nonlinear system which is satisfied with the Bargmannconstraint:u=-<q,q>,v=<∧p.p>is given incidentally.