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Title: The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
Authors: Ferapontov, E.V.
Khusnutdinova, Karima R.
Keywords: mulitdimensional systems of hydrodynamic type
classification of integrable equations
nonlinear interactions of simple waves
generalised hodograph model
Issue Date: 2003
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.
Description: This pre-print has been submitted, and accepted, to the journal, Journal of Physics A- Mathematical and General [© Institute of Physics]. The definitive version: FERAPONTOV, E.V. and KHUSNUTDINOVA,K.R., 2004. The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type. Journal of Physics A- Mathematical and General, 37(8), pp. 2949-2963, is available at: http://www.iop.org/EJ/journal/JPhysA.
URI: https://dspace.lboro.ac.uk/2134/300
Appears in Collections:Pre-prints (Maths)

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