规范变换与有限维可积系统间的变换  

THE GAUGE TRANSFORMATION AND THE TRANSFORMATION BETWEEN FINITE-DIMENSIONAL INTEGRABLE SYSTEMS

作　　者：曾云波[1] 

机构地区：[1]合肥市中国科技大学数学系,230026

出　　处：《高校应用数学学报（A辑）》1993年第4期339-350,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家基础性研究重大项目"非线性科学"资助项目

摘　　要：本文表明,利用两个特征值问题间的规范变换,不仅可以建立和它们相联系的势的约束之间以及相应的有限维Hamilton系统间的变换关系式,而且可以由一个可积系统的对合守恒积分导出另一个系统的守恒积分并证明其对合性,作为例子,本文给出了和修正的二阶多项式谱问题相联系的两个新的有限维可积系统。By using gauge transformation between two spectral problems, the relation connecting constraints of potentials and the transformation between two finite-dimensional Hamiltonian systems can be established, the integrals of motion for one integrable system can be derived from integrals for another system and shown to be in involution. For examples, two new finite-dimensional integrable Hamiltonian systems associated with modified second-order polynomial spectral problems are presented.

关 键 词：规范变换 可积系统 发展方程 

分 类 号：O175.2[理学—数学]