耦合的Burger’s方程族与一个新的Hamilton可积系

The Coupled Burger's Equation Hierarchy and A New Integrable Hamiltonian System

孤子方程族Lax对的非线性化的发展，使得许多非线性方程的解转化为完全可积的Hamiltonian系统的对合解[1～10]，并由此得到了许多在Liouville意义下的新的完全可积系[2～14]。采用新的约束方法，考虑特征值问题与伴随特征值问题得到了一个完全可积的Hamiltonian系统，并由此得到相关的发展方程族解的对合表示。

It is well known that the nonlinearization development of Lax pairs for soliton equation makes nonlinear equation solution transform into the solution of involution of the Hamiltonian system,and the new integrable system in the Liouville sense can be obtained. In this paper,by means of new constraint,the following eigenvalue problemand the adjoint eigervalue problemare considered,and a completely integrable Hamiltonian system is obtained. The involutive solutions of the evolutive equation are given.