English

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

Exactly Solvable and Integrable Systems 2016-02-08 v1

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.

Keywords

Cite

@article{arxiv.1602.02048,
  title  = {The Gibbons--Tsarev equation: symmetries, invariant solutions, and applications},
  author = {Aleksandra Lelito and Oleg I. Morozov},
  journal= {arXiv preprint arXiv:1602.02048},
  year   = {2016}
}