Integrability of multi-dimensional quasilinear systems

Abstract: Multi-dimensional quasilinear systems play important role in physical applications such as gas dynamics. "Integrability" means existence of infinitely many commuting flows, conservation laws and N-component reductions (which are 1+1 hydrodynamic type systems). By this approach some classification of such quasilinear systems is given. Particular solutions (in some cases general solutions) are found.