2003/05/22 by E. V. Ferapontov, K. R. Khusnutdinova · 2 citations
Physics and Astronomy · #nlin.SI
paper · pdf · doi:10.1007/s00220-004-1079-6
23 pages
arxiv created 2003/05/22 · arxiv updated 2009/11/30
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 one-dimensional 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.