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.

References in corpus (3)

• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
• Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
• Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere property

Cited by in corpus (3)

• Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics
• Lax pairs, recursion operators and bi-Hamiltonian representations of (3+1)-dimensional Hirota type equations
• Recursion operators and bi-Hamiltonian representations of cubic evolutionary (2+1)-dimensional systems