Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


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 Two-Component (2+1)-Dimensional Hydrodynamic-Type 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, 50-204 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 so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A dispersionless Lax formulation is found.

Key words: hydrodynamic-type system; dispersionless Lax representation.

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References

  1. Ferapontov E.V., Khusnutdinova K.R., On the integrability of (2+1)-dimensional quasilinear systems, Comm. Math. Phys. 248 (2004), 187-206, nlin.SI/0305044.
  2. Ferapontov E.V., Khusnutdinova K.R., The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type, J. Phys. A: Math. Gen. 37 (2004), 2949-2963, nlin.SI/0310021.
  3. Ferapontov E.V., Marshall D.G., Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor, Math. Ann. 339 (2007), 61-99, nlin.SI/0505013.
  4. Ferapontov E.V., Moro A., Sokolov V.V., Hamiltonian systems of hydrodynamic type in 2+1 dimensions, Comm. Math. Phys. 285 (2009), 31-65, arXiv:0710.2012.
  5. Odesskii A., Sokolov V., Integrable pseudopotentials related to generalized hypergeometric functions, arXiv:0803.0086.
  6. Odesskii A., Pavlov M.V., Sokolov V.V., A classification of integrable Vlasov-like equations, Theoret. and Math. Phys. 154 (2008), 209-219, arXiv:0710.5655.
  7. 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, 165-174.

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