L-C-Z族孤子方程所对应的完全可积的Bargmann系统

Completely Integrable Bargmann System Associated With the L-C-Z Soliton Hierarchy

本文获得一个新的有限维对合系,并由此证明L-C-Z谱问题(2.1)在Bargmann约束:q=〈ψ_1,ψ_1〉-〈ψ_2,ψ_2〉,r=〈ψ_1,ψ_1〉+〈ψ_2,ψ_2〉下被非线性化为一个Liouville完全可积的新的Hamilton系统。最后,我们给出L-C-Z族方程解的对合表示。

In this paper, a new involutive system is obtained and under the Bargmann constriant: q=<φ_1, φ_1>-<φ_2, φ_2>, r=<φ_1, φ_1>+<φ_2, φ_2>, the L-C-Z spectral problem (2.1) is nonlinearized as a new completely integrable Hamiltonian system in Liouville's sense. Finally, we present the involutive solutions of L-C-Z hierarchy of soliton equations.