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TMF, 2004, Volume 141, Number 2, Pages 208–227 (Mi tmf121)  

This article is cited in 10 scientific papers (total in 10 papers)

One Class of Liouville-Type Systems

D. K. Demskoi

Orel State University

Abstract: We prove that a class of systems with the Lagrangian of the form $L=[g_{ij}(u)u^i_xu^j_t]/2+f(u)$ is of the Liouville type. We construct new integrable Hamiltonian systems related to the symmetries of the hyperbolic systems under consideration by substitutions of the Miura transformation type. For one of the systems obtained, we construct the second-order recursion operator.

Keywords: system of Liouville type, higher pseudoconstants, recursion operator

DOI: https://doi.org/10.4213/tmf121

Full text: PDF file (287 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 141:2, 1509–1527

Bibliographic databases:

Received: 13.10.2003
Revised: 16.03.2004

Citation: D. K. Demskoi, “One Class of Liouville-Type Systems”, TMF, 141:2 (2004), 208–227; Theoret. and Math. Phys., 141:2 (2004), 1509–1527

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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. S. Ya. Startsev, “On the variational integrating matrix for hyperbolic systems”, J. Math. Sci., 151:4 (2008), 3245–3253  mathnet  crossref  mathscinet  zmath  elib  elib
    2. D. K. Demskoi, V. G. Marikhin, A. G. Meshkov, “Lax representations for triplets of two-dimensional scalar fields of the chiral type”, Theoret. and Math. Phys., 148:2 (2006), 1034–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Sergyeyev A, Demskoi D, “Sasa-Satsuma (complex modified Korteweg-de Vries II) and the complex sine-Gordon II equation revisited: Recursion operators, nonlocal symmetries, and more”, Journal of Mathematical Physics, 48:4 (2007), 042702  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Demskoi, D, “On application of Liouville type equations to constructing Backlund transformations”, Journal of Nonlinear Mathematical Physics, 14:1 (2007), 147  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Demskoi, DK, “On non-Abelian Toda A(2)((1)) model and related hierarchies”, Journal of Mathematical Physics, 50:12 (2009), 123516  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. D. K. Demskoi, “Integrals of open two-dimensional lattices”, Theoret. and Math. Phys., 163:1 (2010), 466–471  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    7. Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.  mathnet  crossref
    8. S. Ya. Startsev, “On differential substitutions for evolution systems”, Ufa Math. J., 9:4 (2017), 108–113  mathnet  crossref  isi  elib
    9. Demskoi D.K., “Factorisation of Recursion Operators of Some Lagrangian Systems”, J. Nonlinear Math. Phys., 24:3 (2017), 368–378  crossref  mathscinet  isi  scopus  scopus
    10. S. Ya. Startsev, “Structure of set of symmetries for hyperbolic systems of Liouville type and generalized Laplace invariants”, Ufa Math. J., 10:4 (2018), 103–110  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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