On linear degeneracy of integrable quasilinear systems in higher dimensions

Understand

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 $d\geq 6$.