`Interpolating' differential reductions of multidimensional integrable hierarchies

Details `Interpolating' differential reductions of multidimensional integrable hierarchies `Interpolating' differential reductions of multidimensional integrable hierarchies

2010-11-02

arxiv.org/abs/1011.0631v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Based on the talk at NLPVI, Gallipoli, 15 pages

Scientific paper

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

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