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 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 analogues 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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Communicated by G.W. Gibbons
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Ferapontov, E., Khusnutdinova, K. On the Integrability of (2+1)-Dimensional Quasilinear Systems. Commun. Math. Phys. 248, 187–206 (2004). https://doi.org/10.1007/s00220-004-1079-6
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DOI: https://doi.org/10.1007/s00220-004-1079-6