Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures
Mathematical Physics
2018-03-09 v2 General Relativity and Quantum Cosmology
math.MP
Exactly Solvable and Integrable Systems
Abstract
We show that evolutionary Hirota type Euler-Lagrange equations in (2+1) dimensions have a symplectic Monge-Amp\`ere 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.
Cite
@article{arxiv.1712.01549,
title = {Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures},
author = {Mikhail B. Sheftel and Devrim Yazıcı},
journal= {arXiv preprint arXiv:1712.01549},
year = {2018}
}