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Title: On integrability of (2+1)-dimensional quasilinear systems.
Authors: Ferapontov, E.V.
Khusnutdinova, Karima R.
Keywords: multidimensional systems of hydrodynamic type
classification of integrable equations
nonlinear interactions of simple waves
generalized hodograph method
Issue Date: 2003
Abstract: 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.
Description: 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.
URI: https://dspace.lboro.ac.uk/2134/473
Appears in Collections:Pre-prints (Maths)

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