一个新的含非线性位势的谱问题及可积系

A New Spectral Problem with Nonlinear Potential and Integrable System

对一个新的带非线性位势u2 的特征值问题及相应的辅谱问题进行研究 ,得到一族新的孤子方程 ,并由此导出一个新的 ( 2 + 1)维可积模型 .通过将特征值问题非线性化 ,得到一个完全可积的有限维Hamilton系统 。

Based on the study of a new eigenvalue problem with nonlinear potential u 2 and auxiliary problem,the new soliton hierarchies and a new (2+1)-dimensional integrable model are derived.A new completely integrable finite-dimensional Hamiltonian system is obtained by nonlinearization of the eigenvalue problem.Besides,two hierarchies of involutive conserved integrals are given.