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

Symmetry Integrability and Geometry-Methods and Applications

article

Mikhail B. Sheftel¹  Devrim Yazıcı² 

[1] Department of Physics, Boğaziçi University;Department of Physics, Yıldız Technical University

关键词: Lax pair;    recursion operator;    Hamiltonian operator;    bi-Hamiltonian system;   

DOI  :  10.3842/SIGMA.2018.017

来源: National Academy of Science of Ukraine

【 摘 要 】

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 families of integrable equations converted to two-component form we have constructed Lagrangians, recursion operators and bi-Hamiltonian representations. We have also presented a six-parameter family of tri-Hamiltonian systems.

【 授权许可】

Unknown