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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0310021 (nlin)
[Submitted on 15 Oct 2003]

Title:The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type

Authors:E.V. Ferapontov, K.R. Khusnutdinova
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Abstract: We obtain the necessary and sufficient conditions for a two-component (2+1)-dimensional system of hydrodynamic type to possess infinitely many hydrodynamic reductions. These conditions are in involution, implying that the systems in question are locally parametrized by 15 arbitrary constants. It is proved that all such systems possess three conservation laws of hydrodynamic type and, therefore, are symmetrizable in Godunov's sense. Moreover, all such systems are proved to possess a scalar pseudopotential which plays the role of the `dispersionless Lax pair'. We demonstrate that the class of two-component systems possessing a scalar pseudopotential is in fact identical with the class of systems possessing infinitely many hydrodynamic reductions, thus establishing the equivalence of the two possible definitions of the integrability. Explicit linearly degenerate examples are constructed.
Comments: 15 pages
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:nlin/0310021 [nlin.SI]
  (or arXiv:nlin/0310021v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0310021
Related DOI: https://doi.org/10.1088/0305-4470/37/8/007

Submission history

From: E. V. Ferapontov [view email]
[v1] Wed, 15 Oct 2003 16:22:30 UTC (14 KB)
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