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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 3, Pages 354–363
DOI: https://doi.org/10.4213/tmf6646 (Mi tmf6646) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Interpolating differential reductions of multidimensional integrable hierarchies

L. V. Bogdanov

Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
Full-text PDF (410 kB) Citations (16)
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DOI: https://doi.org/10.4213/tmf6646
Abstract: 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.
Keywords: multidimensional integrable hierarchy, differential reduction, Plebański equation.
Received: 23.06.2011
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 3, Pages 705–713
DOI: https://doi.org/10.1007/s11232-011-0055-5
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. V. Bogdanov, “Interpolating differential reductions of multidimensional integrable hierarchies”, TMF, 167:3 (2011), 354–363; Theoret. and Math. Phys., 167:3 (2011), 705–713
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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