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arXiv · 1011.0631

`Interpolating' differential reductions of multidimensional integrable hierarchies

L. V. Bogdanov
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Abstract

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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L. V. Bogdanov. 2010-11-02. `Interpolating' differential reductions of multidimensional integrable hierarchies. https://doi.org/10.1007/s11232-011-0055-5

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