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

E. V. Ferapontov·K. R. Khusnutdinova
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Abstract

An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type u_t+A(u)u_x+B(u)u_y=0 is developed. It is proved that the existence of special solutions known as `double waves' is equivalent to the diagonalizability of an arbitrary matrix of the two-parameter family (kE+A)^{-1}(lE+B). Since the diagonalizability can be effectively verified by differential-geometric means, this provides a simple necessary condition for integrability.

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E. V. Ferapontov, K. R. Khusnutdinova. 2005-11-29. Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability. https://arxiv.org/abs/nlin/0412064

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