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

preprint

posted on 2005-09-19, 16:41 authored 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.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

195456 bytes## Publication date

2003## Notes

This pre-print has been submitted, and accepted, to the journal, Communications in Mathematical Physics [© Springer]. The definitive version: FERAPONTOV, E.V. and KHUSNUTDINOVA, K.R., 2004. On integrability of (2+1)-dimensional quasilinear systems. Communciations in Mathematical Physics, 248(1), pp.187-206, is available at: http://www.springerlink.com/openurl.asp?genre=journal&eissn=1432-0916.## Language

- en