Three dimensional reductions of four-dimensional quasilinear systems

In this paper, we show that four-dimensional quasilinear systems of first order integrable by the method of two-dimensional hydrodynamic reductions possess infinitely many three-dimensional hydrodynamic reductions, which are also integrable systems. These three-dimensional multi-component integrable systems are irreducible to twodimensional hydrodynamic reductions in a generic case.