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

preprint
posted on 19.09.2005, 16:41
A (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.

• Science

## Department

• Mathematical Sciences

195456 bytes

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.

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