
SIGMA 5 (2009), 011, 10 pages arXiv:0901.4312
https://doi.org/10.3842/SIGMA.2009.011
Contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries
On Integrability of a Special Class of TwoComponent (2+1)Dimensional HydrodynamicType Systems
Maxim V. Pavlov ^{a} and Ziemowit Popowicz ^{b}
^{a)} Department of Mathematical Physics, P.N. Lebedev Physical Institute of RAS,
53 Leninskii Ave., 119991 Moscow, Russia
^{b)} Institute of Theoretical Physics, University of Wroclaw,
pl. M. Borna 9, 50204 Wroclaw, Poland
Received August 28, 2008, in final form January 20, 2009; Published online January 27, 2009
Abstract
The particular case of the integrable two component (2+1)dimensional
hydrodynamical type systems, which generalises the socalled Hamiltonian
subcase, is considered. The associated system in
involution is integrated in a parametric form. A dispersionless Lax
formulation is found.
Key words:
hydrodynamictype system; dispersionless Lax representation.
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References
 Ferapontov E.V., Khusnutdinova K.R., On
the integrability of (2+1)dimensional quasilinear systems, Comm. Math. Phys.
248 (2004), 187206, nlin.SI/0305044.
 Ferapontov E.V., Khusnutdinova K.R., The
characterization of twocomponent (2+1)dimensional integrable systems of
hydrodynamic type, J. Phys. A: Math. Gen. 37 (2004), 29492963, nlin.SI/0310021.
 Ferapontov E.V., Marshall D.G.,
Differentialgeometric approach to the integrability of hydrodynamic chains:
the Haantjes tensor, Math. Ann. 339 (2007), 6199, nlin.SI/0505013.
 Ferapontov E.V., Moro A., Sokolov V.V.,
Hamiltonian systems of hydrodynamic type in 2+1 dimensions, Comm. Math.
Phys. 285 (2009), 3165, arXiv:0710.2012.
 Odesskii A., Sokolov V., Integrable
pseudopotentials related to generalized hypergeometric functions, arXiv:0803.0086.
 Odesskii A., Pavlov M.V., Sokolov V.V., A
classification of integrable Vlasovlike equations, Theoret. and Math. Phys. 154
(2008), 209219, arXiv:0710.5655.
 Zakharov V.E., Dispersionless limit of
integrable systems in 2+1 dimensions, in Singular Limits of Dispersive
Waves (Lyon, 1991), Editors N.M. Ercolani et al., NATO Adv. Sci. Inst. Ser. B Phys., Vol. 320, Plenum, New York, 1994, 165174.

