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Title: Double waves in multi-dimensional systems of hydrodynamic type: the necessary condition for integrability
Authors: Ferapontov, E.V.
Khusnutdinova, Karima R.
Keywords: multi-dimensional systems of hydrodynamic type
Riemann invariants
Haantjes tensor
nonlinear interactions of planar simple waves
double waves
Issue Date: 2005
Abstract: 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 as `double waves' is generically equivalent to the diagonalizability of an arbitrary matrix of some two-parameter family of matrices associated with the system. Since the diagonalizability can be effectively verified by differential-geometric means, this provides a simple necessary condition for integrability.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/410
Appears in Collections:Pre-prints (Maths)

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