Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Sheftel, M.B., Yazici, D.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209447
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures / M.B. Sheftel, D. Yazici // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ.

We show that evolutionary Hirota-type Euler-Lagrange equations in (2+1) dimensions have a symplectic Monge-Ampère form. We consider integrable equations of this type in the sense that they admit infinitely many hydrodynamic reductions and determine Lax pairs for them. For two seven-parameter familie...