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

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Sheftel M. B., YAZICI D.

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

  • 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
  • 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.