非等谱Lax算子族的Virasoro代数

VIRASORO ALGEBRAS OF THE HIERARCHIES OFNONISOSPECTRAL LAX OPERATORS

非等谱Ｌａｘ算子族的Ｖｉｒａｓｏｒｏ代数马文秀（复旦大学数学研究所，上海２００４３３）国家博士后科学基金资助项目．１９９１年７月２５日收到．１９９２年７月６日收到修改稿．一、引言Ｌａｘ算子方法［１］在可积系统理论中有着广泛的应用．从一个谱问题出发我们...

ABSTRACTA theoretical description of nonisospectral Lax representations is presented fora hierarchy of systems with Lenard recursive structure. On the basis of this description, it is shown that under rather general conditions, the corresponding hierarchy of nonisospectral Lax operators constitutes a Virasoro algebra, and further it isderived that the hierarchy of nonisospectral systems constitutes the same Virasoro algebra. Finally, an illustrative example is given.