No abstract

We study nonlocal symmetries of Plebański's second heavenly equation in an infinite-dimensional covering associated to a Lax pair with a non-removable spectral parameter. We show that all local symmetries of the equation admit lifts to full-fledged nonlocal symmetries in the infinite-dimensional covering. Also, we find two new infinite hierarchies of commuting nonlocal symmetries in this covering and describe the structure of the Lie algebra of the obtained nonlocal symmetries.

No abstract

Abstract. 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. Gibbons-Tsarev equation: symmetries, invariant solutions, and applications2

No abstract