ferapontov_characterisation.pdf (188.44 kB)

Download file# The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type

preprint

posted on 29.07.2005, 15:35 by Evgeny FerapontovEvgeny Ferapontov, Karima KhusnutdinovaKarima KhusnutdinovaWe 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.

## History

## School

- Science

## Department

- Mathematical Sciences