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Double waves in multi-dimensional systems of hydrodynamic type: the necessary condition for integrability

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preprint
posted on 2005-08-17, 09:48 authored by E.V. Ferapontov, Karima R. Khusnutdinova
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.

History

School

  • Science

Department

  • Mathematical Sciences

Pages

207826 bytes

Publication date

2005

Notes

This is a pre-print.

Language

  • en