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

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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.

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Authors and Affiliations

  1. Korteweg-de Vries Institute, University of Amsterdam, Amsterdam, The Netherlands

    G. F. Helminck

  2. North Carolina State University, Raleigh, North Carolina, USA

    A. G. Helminck

  3. Derzhavin Tambov State University, Tambov, Russia

    E. A. Panasenko

Authors
  1. G. F. Helminck
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  2. A. G. Helminck
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  3. E. A. Panasenko
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Corresponding author

Correspondence to G. F. Helminck.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 174, No. 1, pp. 154–176, January, 2013.

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Helminck, G.F., Helminck, A.G. & Panasenko, E.A. Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective. Theor Math Phys 174, 134–153 (2013). https://doi.org/10.1007/s11232-013-0011-7

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  • DOI: https://doi.org/10.1007/s11232-013-0011-7

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