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


Sheftel M. B. , YAZICI D.

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.14, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14
  • Publication Date: 2018
  • Doi Number: 10.3842/sigma.2018.017
  • Title of Journal : SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS

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.