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TMF, 2005, Volume 144, Number 1, Pages 35–43 (Mi tmf1829)  

This article is cited in 13 scientific papers (total in 13 papers)

Classification of Integrable $(2+1)$-Dimensional Quasilinear Hierarchies

E. V. Ferapontovab, K. R. Khusnutdinovabc, M. V. Pavlovb

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Loughborough University
c Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences

Abstract: We investigate the $(2+1)$-dimensional hierarchies associated with the integrable PDEs of the form $\Omega_{tt}=F(\Omega_{xx},\Omega_{xt},\Omega_{xy})$, which generalize the dispersionless KP hierarchy. Integrability is understood as the existence of infinitely many hydrodynamic reductions.

Keywords: integrable hierachies of dKP type, hydrodynamic reductions, pseudopotentials

DOI: https://doi.org/10.4213/tmf1829

Full text: PDF file (216 kB)
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English version:
Theoretical and Mathematical Physics, 2005, 144:1, 907–915

Bibliographic databases:


Citation: E. V. Ferapontov, K. R. Khusnutdinova, M. V. Pavlov, “Classification of Integrable $(2+1)$-Dimensional Quasilinear Hierarchies”, TMF, 144:1 (2005), 35–43; Theoret. and Math. Phys., 144:1 (2005), 907–915

Citation in format AMSBIB
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\paper Classification of Integrable $(2+1)$-Dimensional Quasilinear Hierarchies
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pavlov MV, “Classification of integrable hydrodynamic chains and generating functions of conservation laws”, Journal of Physics A-Mathematical and General, 39:34 (2006), 10803–10819  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Ferapontov EV, Khusnutdinova KR, Tsarev SP, “On a class of three-dimensional integrable Lagrangians”, Communications in Mathematical Physics, 261:1 (2006), 225–243  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. M. V. Pavlov, “Integrability of the Egorov systems of hydrodynamic type”, Theoret. and Math. Phys., 150:2 (2007), 225–243  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. E. Adler, A. B. Shabat, “Model equation of the theory of solitons”, Theoret. and Math. Phys., 153:1 (2007), 1373–1387  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Ferapontov EV, Marshall DG, “Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor”, Mathematische Annalen, 339:1 (2007), 61–99  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Zenchuk, AI, “Lower-dimensional reductions of GL(M,C) self-dual Yang Mills equation: Solutions with break of wave profiles”, Journal of Mathematical Physics, 49:6 (2008), 063502  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Ferapontov, EV, “Dispersive deformations of hydrodynamic reductions of (2+1)D dispersionless integrable systems”, Journal of Physics A-Mathematical and Theoretical, 42:3 (2009), 035211  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Ferapontov E.V., Hadjikos L., Khusnutdinova K.R., “Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian”, Int. Math. Res. Not. IMRN, 2010, no. 3, 496–535  crossref  mathscinet  zmath  isi  scopus
    9. Burovskiy P.A., Ferapontov E.V., Tsarev S.P., “Second-order quasilinear PDEs and conformal structures in projective space”, Internat. J. Math., 21:6 (2010), 799–841  crossref  mathscinet  zmath  isi  elib  scopus
    10. V. M. Zhuravlev, “Multidimensional nonlinear wave equations with multivalued solutions”, Theoret. and Math. Phys., 174:2 (2013), 236–246  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. V. M. Zhuravlev, “Multidimensional quasilinear first-order equations and multivalued solutions of the elliptic and hyperbolic equations”, Theoret. and Math. Phys., 186:3 (2016), 320–332  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. Doubrov B., Ferapontov E.V., Kruglikov B., Novikov V.S., “On Integrability in Grassmann Geometries: Integrable Systems Associated With Fourfolds in Gr(3,5)”, Proc. London Math. Soc., 116:5 (2018), 1269–1300  crossref  mathscinet  zmath  isi  scopus
    13. M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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