The Gibbons--Tsarev equation: symmetries, invariant solutions, and applications

In this paper we present the full classification of the symmetry-invariant solutions for the Gibbons--Tsarev equation. Then we use these solutions to construct explicit expressions for reductions of Benney's moments equations, to get solutions of Pavlov's equation, and to find integrable reductions of the Ferapontov--Huard--Zhang system, which describes implicit two-phase solutions of the dKP equation.