4 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 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…
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…