6 papers
Discrete integrable equations with three independent variables
Ismagil T. Habibullin, Aigul R. Khakimova
In this paper, we study nonlinear integrable equations with three independent variables of the following types: Toda-type lattices, semi-discrete lattices, and fully discrete Hirot…
On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries
R. N. Garifullin, I. T. Habibullin
This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continu…
On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain
I. T. Habibullin, A. R. Khakimova
An effective method for constructing explicit solutions to the Davey--Stewartson type integrable equations is discussed based on the use of a dressing chain. The application of the…
On a class of exact solutions of the Ishimori equation
Rustem N. Garifullin, Ismagil T. Habibullin
In this paper, a class of particular solutions of the Ishimori equation is found. This equation is known as the spatially two-dimensional version of the Heisenberg equation, which…
Construction of exact solutions of nonlinear PDE via dressing chain in 3D
I. T. Habibullin, A. R. Khakimova
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recentl…
Higher symmetries of the lattices in 3D
I. T. Habibullin, A. R. Khakimova
It is known that there is a duality between the Davey--Stewartson type coupled systems and a class of integrable two--dimensional Toda type lattices. More precisely, the coupled sy…