# 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}
}
• Published 2005
• Physics, Mathematics
• Mathematische Annalen
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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Abstract We consider hydrodynamic chains in (1+1) dimensions which are Hamiltonian with respect to the Kupershmidt–Manin Poisson bracket. These systems can be derived from single (2+1) equations,Expand
The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
• Mathematics
• Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• 2006
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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We characterize a class of integrable Hamiltonian hydrodynamic chains, based on the necessary condition for the integrability provided by the vanishing of the Haantjes tensor. We prove that theExpand
Double waves in multi-dimensional systems of hydrodynamic type: the necessary condition for integrability
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The invariant differential-geometric approach to the integrability of (2+1)- dimensional systems of hydrodynamic type is developed. It is argued that the existence of special solutions known asExpand
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