A new class of exact solutions for three-dimensional quasilinear systems of first order

Well-known Lin–Reissner–Tsien equation in aerodynamics (1948) will be considered. This equation also is known as the Khokhlov–Zabolotskaya equation in nonlinear acoustics, and is known as a dispersionless limit of the Kadomtsev–Petviashvili equation in hydrodynamics.
New ansatz for construction of infinitely many two-dimensional reductions is found for this three-dimensional equation. They are generalisations of two-dimensional hydrodynamic reductions.
In one-component case, a corresponding particular solution is found with five arbitrary functions of a single variable.
Also some other three-dimensional integrable quasilinear systems of first order will be considered.