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

---

Copy For Citation

Sheftel M. B., YAZICI D.

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.14, 2018 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 14
• Publication Date: 2018
• Doi Number: 10.3842/sigma.2018.017
• Journal Name: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Keywords: Lax pair, recursion operator, Hamiltonian operator, bi-Hamiltonian system
• Yıldız Technical University Affiliated: Yes

Abstract

We show that evolutionary Hirota type Euler Lagrange equations in (2 + 1) dimensions have a symplectic Monge Ampere 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.