Volume 23, Issue 2, March 2016, Pages 243 - 255
The Gibbons–Tsarev equation: symmetries, invariant solutions, and applications
Authors
Aleksandra Lelito
Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, Cracow 30-059, Poland,alelito@agh.edu.pl
Oleg I. Morozov
Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, Cracow 30-059, Poland,morozov@agh.edu.pl
Received 5 February 2016, Accepted 22 February 2016, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1175821How to use a DOI?
- Keywords
- Gibbons-Tsarev equation; symmetries; invariant solutions
- Abstract
In this paper we present the full classification of symmetry-invariant solutions for the Gibbons–Tsarev equation. Then we use these solutions to construct explicit expressions for two-component 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.
- Copyright
- © 2016 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Aleksandra Lelito AU - Oleg I. Morozov PY - 2021 DA - 2021/01/06 TI - The Gibbons–Tsarev equation: symmetries, invariant solutions, and applications JO - Journal of Nonlinear Mathematical Physics SP - 243 EP - 255 VL - 23 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1175821 DO - 10.1080/14029251.2016.1175821 ID - Lelito2021 ER -