  In this paper we show that integrable four dimensional linearly degenerate
equations of second order possess infinitely many three dimensional
hydrodynamic reductions. Furthermore, they are equipped infinitely many
conservation laws and higher commuting flows. We show that the dispersionless
limits of nonlocal KdV and nonlocal NLS equations (the so-called Breaking
Soliton equations introduced by O.I. Bogoyavlenski) are one and two component
reductions (respectively) of one of these four dimensional linearly degenerate
equations.
