拟Wrongsky行列式与扩张的KP及KdV可积序列

QUASI-WRONGSKY DETERMINANTES AND EXTENDED KP AND KdV HIERARCHIES

将Sato关于KP和KdV可积序列的理论推广到矩阵Lax算子的情形,得到一批我们称之为扩张的KP和KdV序列的新可积方程族。从构造过程可以得知,这些新可积方程族的解可以用我们所称的拟Wrongsky行列式来表达,而这种拟Wrongsky行列式正是不久前我们研究2阶扩张的广义Toda方程的解时得到的。

The Sato theory of KP and KdV hierarchies is generalized to the case of matrix lax operators , leading to new hierarchies of integrable nonlinear partial differential equations, which are called extended KP and KdV hierarchies in the context. It can be seen from the construction Process, the solutions of these new hierarchies can be expressed by the so-called quasi-wrongsky determinartes, and these quasi-wrongsky determinantes are just those obtained in ou recent study of 2-extended Toda field theories.