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Download fileOn 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 bytesPublication date
2003Notes
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