On the Integrability of (2+1)-Dimensional Quasilinear Systems

@article{Ferapontov2004OnTI,
  title={On the Integrability of (2+1)-Dimensional Quasilinear Systems},
  author={E. Ferapontov and K. Khusnutdinova},
  journal={Communications in Mathematical Physics},
  year={2004},
  volume={248},
  pages={187-206}
}
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… Expand
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