Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, cilt.14, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14
- Basım Tarihi: 2018
- Doi Numarası: 10.3842/sigma.2018.017
- Dergi Adı: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: Lax pair, recursion operator, Hamiltonian operator, bi-Hamiltonian system
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
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.