Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor

@article{Ferapontov2005DifferentialgeometricAT,
  title={Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor},
  author={Eugene V. Ferapontov and D. G. Marshall},
  journal={Mathematische Annalen},
  year={2005},
  volume={339},
  pages={61-99}
}
The integrability of an m-component system of hydrodynamic type, ut = V(u)ux, by the generalized hodograph method requires the diagonalizability of the m ×  m matrix V(u). This condition is known to be equivalent to the vanishing of the corresponding Haantjes tensor. We generalize this approach to hydrodynamic chains—infinite-component systems of hydrodynamic type for which the ∞ ×  ∞ matrix V(u) is ‘sufficiently sparse’. For such systems the Haantjes tensor is well-defined, and the calculation… Expand
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The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type,is developed. We prove that the existence of special solutions known as ‘doubleExpand
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Double waves in multi-dimensional systems of hydrodynamic type: the necessary condition for integrability
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