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

Abstract

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.