59 citations · 311 across the 29 of their papers we have counts for
29 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…
Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors
Mikhail B. Sheftel
The complex Monge-Ampère equation in a two-component form is treated as a bi-Hamiltonian system. I present explicitly the first nonlocal symmetry flow in each of the two hi…
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…
Inflation and Linear Expansion in the Radiation Dominated era in Jordan-Brans-Dicke Cosmology
Metin Arik, Medine Ildes, Mikhail B. Sheftel
We present several features of a cosmological model based on the Brans-Dicke-Jordan-Thirry action which is scale invariant with a quartic potential for the Jordan scalar field. We…
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…