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

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

2003-05-22

arxiv.org/abs/nlin/0305044v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

23 pages

Scientific paper

10.1007/s00220-004-1079-6

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.

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