Interpolating differential reductions of multidimensional integrable hierarchies

摘要

We apply the scheme for constructing differential reductions recently developed for the Manakov-Santini hierarchy to the general multidimensional case. We consider the four-dimensional case connected with the second heavenly equation and its generalization proposed by Dunajski in more detail. We characterize differential reductions in terms of the Lax-Sato equations and also in the framework of the dressing method based on the nonlinear Riemann-Hilbert problem.