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

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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 1, Pages 35–43
DOI: https://doi.org/10.4213/tmf1829 (Mi tmf1829)

This article is cited in 18 scientific papers (total in 18 papers)

Classification of Integrable

(2 + 1)

$(2+1)$ -Dimensional Quasilinear Hierarchies

E. V. Ferapontov^ab, K. R. Khusnutdinova^bc, M. V. Pavlov^b

^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

Full-text PDF (216 kB) Citations (18)

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

Abstract: We investigate the

(2 + 1)

$(2+1)$ -dimensional hierarchies associated with the integrable PDEs of the form

Ω_{t t} = F (Ω_{x x}, Ω_{x t}, Ω_{x y})

$\Omega_{tt}=F(\Omega_{xx},\Omega_{xt},\Omega_{xy})$ , 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.

English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 1, Pages 907–915
DOI: https://doi.org/10.1007/s11232-005-0117-7

Bibliographic databases:

Language: Russian

Citation: E. V. Ferapontov, K. R. Khusnutdinova, M. V. Pavlov, “Classification of Integrable

(2 + 1)

$(2+1)$ -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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Linking options:

https://www.mathnet.ru/eng/tmf1829

https://doi.org/10.4213/tmf1829

https://www.mathnet.ru/eng/tmf/v144/i1/p35

This publication is cited in the following 18 articles:

Ismagil T. Habibullin, Aigul R. Khakimova, “Higher Symmetries of Lattices in 3D”, Regul. Chaotic Dyn., 29:6 (2024), 853–865
I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices via Lie–Rinehart algebras”, Theoret. and Math. Phys., 203:1 (2020), 569–581
Habibullin I.T., Kuznetsova M.N., Sakieva A.U., “Integrability Conditions For Two-Dimensional Toda-Like Equations”, J. Phys. A-Math. Theor., 53:39 (2020), 395203
Clery F., Ferapontov V E., “Dispersionless Hirota Equations and the Genus 3 Hyperelliptic Divisor”, Commun. Math. Phys., 376:2 (2020), 1397–1412
Ufa Math. J., 11:3 (2019), 109–131
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
M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105
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
V. M. Zhuravlev, “Multidimensional nonlinear wave equations with multivalued solutions”, Theoret. and Math. Phys., 174:2 (2013), 236–246
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
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
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
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
M. V. Pavlov, “Integrability of the Egorov systems of hydrodynamic type”, Theoret. and Math. Phys., 150:2 (2007), 225–243
V. E. Adler, A. B. Shabat, “Model equation of the theory of solitons”, Theoret. and Math. Phys., 153:1 (2007), 1373–1387
Ferapontov EV, Marshall DG, “Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor”, Mathematische Annalen, 339:1 (2007), 61–99
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
Ferapontov EV, Khusnutdinova KR, Tsarev SP, “On a class of three-dimensional integrable Lagrangians”, Communications in Mathematical Physics, 261:1 (2006), 225–243

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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