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Lie-algebraic structure of (2 + 1)-dimensional Lax-type integrable nonlinear dynamical systems

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Abstract

A Hamiltonian representation for a hierarchy of Lax-type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems is obtained via some special Båcklund transformation. The connection of this hierarchy with Lax-integrable two-metrizable systems is studied.

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Authors and Affiliations

  1. Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv

    A. K. Prykarpats’kyi & O. E. Hentosh

  2. ACH, KrakÓw, Poland

    A. K. Prykarpats’kyi

Authors
  1. A. K. Prykarpats’kyi
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  2. O. E. Hentosh
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 939–946, July, 2004.

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Prykarpats’kyi, A.K., Hentosh, O.E. Lie-algebraic structure of (2 + 1)-dimensional Lax-type integrable nonlinear dynamical systems. Ukr Math J 56, 1117–1126 (2004). https://doi.org/10.1007/s11253-005-0121-y

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  • DOI: https://doi.org/10.1007/s11253-005-0121-y

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