On linear degeneracy of integrable quasilinear systems in higher dimensions

E. V. Ferapontov; K. R. Khusnutdinova; C. Klein

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arXiv · 0909.5685

On linear degeneracy of integrable quasilinear systems in higher dimensions

E. V. Ferapontov·K. R. Khusnutdinova·C. Klein

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Abstract

We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be linearly degenerate. We prove this conjecture in the 2-component case, providing a complete classification of multi-dimensional integrable systems in question. In particular, our results imply the non-existence of 2-component integrable systems of hydrodynamic type for $d\geq 6$. In the second half of the paper we discuss a numerical and analytical evidence for the impossibility of the breakdown of smooth initial data for linearly degenerate systems in 2+1 dimensions.

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E. V. Ferapontov, K. R. Khusnutdinova, C. Klein. 2010-03-09. On linear degeneracy of integrable quasilinear systems in higher dimensions. https://arxiv.org/abs/0909.5685

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