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Download file# On integrability of (2+1)-dimensional quasilinear systems.

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posted on 19.09.2005, 16:41 by Evgeny FerapontovEvgeny Ferapontov, Karima KhusnutdinovaKarima KhusnutdinovaA (2+1)-dimensional quasilinear system is said to be ‘integrable’ if it can be
decoupled in infinitely many ways into a pair of compatible n-component onedimensional
systems in Riemann invariants. Exact solutions described by these
reductions, known as nonlinear interactions of planar simple waves, can be viewed
as natural dispersionless analogs of n-gap solutions. It is demonstrated that the
requirement of the existence of ‘sufficiently many’ n-component reductions provides
the effective classification criterion. As an example of this approach we classify
integrable (2+1)-dimensional systems of conservation laws possessing a convex
quadratic entropy.

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