A CLASS OF MULTIDIMENSIONAL INTEGRABLE HIERARCHIES AND THEIR REDUCTIONS

摘要

We consider a class of multidimensional integrable hierarchies connected with the commutativity of general (unreduced) (N+1)-dimensional vector fields containing a derivative with respect to a spectral variable.These hierarchies are determined by a generating equation, equivalent to the Lax–Sato form. We present a dressing scheme based on a nonlinear vector Riemann problem for this class. As characteristic examples,we consider the hierarchies connected with the Manakov–Santini equation and the Dunajski system.