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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 1, Pages 15–22
DOI: https://doi.org/10.4213/tmf6374 (Mi tmf6374) 		 
This article is cited in 13 scientific papers (total in 13 papers)

A class of multidimensional integrable hierarchies and their reductions

L. V. Bogdanov

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (371 kB) Citations (13)
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DOI: https://doi.org/10.4213/tmf6374
Abstract: 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.
Keywords: integrable hierarchy, dispersionless equation, heavenly equation, dressing method.
English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 1, Pages 887–893
DOI: https://doi.org/10.1007/s11232-009-0078-3
Bibliographic databases:
Language: Russian
Citation: L. V. Bogdanov, “A class of multidimensional integrable hierarchies and their reductions”, TMF, 160:1 (2009), 15–22; Theoret. and Math. Phys., 160:1 (2009), 887–893
Citation in format AMSBIB
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\transl
\jour Theoret. and Math. Phys.
\yr 2009
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\issue 1
\pages 887--893
\crossref{https://doi.org/10.1007/s11232-009-0078-3}
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    • This publication is cited in the following 13 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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    References:74
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