16 citations · 56 across the 10 of their papers we have counts for
10 papers
Recursion operators and bi-Hamiltonian representations of cubic evolutionary (2+1)-dimensional systems
M. B. Sheftel, D. Yazıcı
We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We conver…
Symmetries, integrals and hierarchies of new (3+1)-dimensional bi-Hamiltonian systems of Monge--Ampère type
Mikhail Sheftel, Devrim Yazıcı
We study point symmetries, the corresponding conserved densities and hierarchies of four new bi-Hamiltonian heavenly systems in 3+1 dimensions which we discovered recently. We exhi…
Lax pairs, recursion operators and bi-Hamiltonian representations of (3+1)-dimensional Hirota type equations
M. B. Sheftel, D. Yazıcı
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown enters only in the form of the 2nd-order partial derivatives. For such equations which possess a…
Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures
Mikhail B. Sheftel, Devrim Yazıcı
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 t…
Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
Mikhail B. Sheftel, Devrim Yazıcı
We present first heavenly equation of Plebański in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmet…
Recursion operators and bi-Hamiltonian structure of the general heavenly equation
M. B. Sheftel, A. A. Malykh, D. Yazıcı
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equ…
Anti-self-dual gravity from asymmetric heavenly equation standpoint
M. B. Sheftel, D. Yazıcı
In paper [3] on the classification of second-order PDEs with four independent variables that possess partner symmetries, asymmetric heavenly equation appears as one of canonical eq…
Bi-Hamiltonian representation, symmetries and integrals of mixed heavenly and Husain systems
M. B. Sheftel, D. Yazici
In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries (J. Phys…
Self-dual gravity is completely integrable
Y. Nutku, M. B. Sheftel, J. Kalayci +1
We discover multi-Hamiltonian structure of complex Monge-Ampere equation (CMA) set in a real first-order two-component form. Therefore, by Magri's theorem this is a completely inte…
Multicomponent bi-superHamiltonian KdV systems
Devrim Yazici, Oya Oguz, Omer Oguz
It is shown that a new class of classical multicomponent super KdV equations is bi-superHamiltonian by extending the method for the verification of graded Jacobi identity. The mult…