Volume 17, Issue 4, December 2010, Pages 453 - 484
Bi-Hamiltonian Representation, Symmetries and Integrals of Mixed Heavenly and Husain Systems
Authors
M. B. Sheftel
Physics Department, Boğaziçi University, 34342 Bebek, Istanbul, Turkey,mikhail.sheftel@boun.edu.tr
D. Yazici
Physics Department, Yıldız Technical University, 34220 Esenler, Istanbul, Turkey,yazici@yildiz.edu.tr
Received 10 August 2009, Accepted 27 April 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110001021How to use a DOI?
- Keywords
- Symmetries; integrals; Noether theorem; Lax pair; symplectic two-form; bi-Hamiltonian representation
- Abstract
In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation and Husain equation appear as closely related canonical equations admitting partner symmetries. Here for the mixed heavenly equation and Husain equation, formulated in a two-component form, we present recursion operators, Lax pairs of Olver–Ibragimov–Shabat type and discover their Lagrangians, symplectic and bi-Hamiltonian structure. We obtain all point and second-order symmetries, integrals and bi-Hamiltonian representations of these systems and their symmetry flows together with infinite hierarchies of nonlocal higher symmetries.
- Copyright
- © 2010 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 - M. B. Sheftel AU - D. Yazici PY - 2021 DA - 2021/01/07 TI - Bi-Hamiltonian Representation, Symmetries and Integrals of Mixed Heavenly and Husain Systems JO - Journal of Nonlinear Mathematical Physics SP - 453 EP - 484 VL - 17 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110001021 DO - 10.1142/S1402925110001021 ID - Sheftel2021 ER -