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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 136, Number 2, Pages 197–208
DOI: https://doi.org/10.4213/tmf225 (Mi tmf225) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Universal Models of Soliton Hierarchies

A. B. Shabat

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (227 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf225
Abstract: We consider commutativity equations and a related new model similar to the Kadomtsev–Petviashvili equation in the Sato theory. Integration of this model equation with three independent variables is based on a generalization of the Dubrovin equations and the recently developed theory of transformations of spectral problems. We give examples of equations with a fractional-power dispersion law that can be linearized in this theory.
Keywords: commutativity equations, Dubrovin equations, classical hierarchies.
Received: 16.12.2002
English version:
Theoretical and Mathematical Physics, 2003, Volume 136, Issue 2, Pages 1066–1076
DOI: https://doi.org/10.1023/A:1025057719859
Bibliographic databases:
Language: Russian
Citation: A. B. Shabat, “Universal Models of Soliton Hierarchies”, TMF, 136:2 (2003), 197–208; Theoret. and Math. Phys., 136:2 (2003), 1066–1076
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf225
  • https://doi.org/10.4213/tmf225
  • https://www.mathnet.ru/eng/tmf/v136/i2/p197
    • This publication is cited in the following 5 articles:
    1. Konopelchenko B.G. Ortenzi G., “Parabolic Regularization of the Gradient Catastrophes For the Burgers-Hopf Equation and Jordan Chain”, J. Phys. A-Math. Theor., 51:27 (2018), 275201  crossref  mathscinet  isi  scopus  scopus
    2. Sergyeyev A, Szablikowski BM, “Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems”, Physics Letters A, 372:47 (2008), 7016–7023  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Levi D, Winternitz P, “Continuous symmetries of difference equations”, Journal of Physics A-Mathematical and General, 39:2 (2006), R1–R63  crossref  mathscinet  zmath  isi  scopus  scopus
    4. S. B. Leble, “Necessary Covariance Conditions for a One-Field Lax Pair”, Theoret. and Math. Phys., 144:1 (2005), 985–994  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. L. Martínez Alonso, A. B. Shabat, “Hydrodynamic Reductions and Solutions of a Universal Hierarchy”, Theoret. and Math. Phys., 140:2 (2004), 1073–1085  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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