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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 1, Pages 154–176
DOI: https://doi.org/10.4213/tmf8362 (Mi tmf8362) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective

G. F. Helmincka, A. G. Helminckb, E. A. Panasenkoc

a Korteweg-de~Vries Institute, University of Amsterdam, Amsterdam, The Netherlands
b North Carolina State University, Raleigh, USA
c Derzhavin Tambov State University, Tambov, Russia
Full-text PDF (475 kB) Citations (16)
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DOI: https://doi.org/10.4213/tmf8362
Abstract: We split the algebra of pseudodifferential operators in two different ways into the direct sum of two Lie subalgebras and deform the set of commuting elements in one subalgebra in the direction of the other component. The evolution of these deformed elements leads to two compatible systems of Lax equations that both have a minimal realization. We show that this Lax form is equivalent to a set of zero-curvature relations. We conclude by presenting linearizations of these systems, which form the key framework for constructing the solutions.
Keywords: integrable deformation, pseudodifferential operator, Lax equation, Kadomtsev–Petviashvili hierarchy, zero-curvature relation, linearization.
Received: 14.05.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 1, Pages 134–153
DOI: https://doi.org/10.1007/s11232-013-0011-7
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. F. Helminck, A. G. Helminck, E. A. Panasenko, “Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective”, TMF, 174:1 (2013), 154–176; Theoret. and Math. Phys., 174:1 (2013), 134–153
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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