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TMF, 2002, Volume 130, Number 1, Pages 15–30 (Mi tmf288)  

This article is cited in 4 scientific papers (total in 4 papers)

Integrable Chains and Hierarchies of Differential Evolution Equations

A. K. Svinin

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: A class of integrable differential-difference systems is constructed based on auxiliary linear equations defined on sequences of Zakharov–Shabat formal dressing operators. We show that the auxiliary equations are compatible with the evolution equations for the Kadomtsev–Petviashvili (KP) hierarchy. The investigation results are used to elaborate a modified version of Krichever rational reductions for KP hierarchies.

DOI: https://doi.org/10.4213/tmf288

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English version:
Theoretical and Mathematical Physics, 2002, 130:1, 11–24

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Received: 16.04.2001

Citation: A. K. Svinin, “Integrable Chains and Hierarchies of Differential Evolution Equations”, TMF, 130:1 (2002), 15–30; Theoret. and Math. Phys., 130:1 (2002), 11–24

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Svinin, AK, “A class of integrable lattices and KP hierarchy”, Journal of Physics A-Mathematical and General, 34:48 (2001), 10559  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Cieslinski, JL, “Darboux covariant equations of von Neumann type and their generalizations”, Journal of Mathematical Physics, 44:4 (2003), 1763  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. A. K. Svinin, “Invariant Submanifolds of the Darboux–Kadomtsev–Petviashvili Chain and an Extension of the Discrete Kadomtsev–Petviashvili Hierarchy”, Theoret. and Math. Phys., 141:2 (2004), 1542–1561  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Ustinov NV, “The lattice equations of the Toda type with an interaction between a few neighbourhoods”, Journal of Physics A-Mathematical and General, 37:5 (2004), 1737–1746  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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