19 citations · 36 across the 6 of their papers we have counts for
6 papers
Discrete exponential type systems on a quad graph, corresponding to the affine Lie algebras
I T Habibullin, A R Khakimova
The article deals with the problem of the integrable discretization of the well-known Drinfeld-Sokolov hierarchies related to the Kac-Moody algebras. A class of discrete exponentia…
Algebraic Properties of Quasilinear Two-Dimensional Lattices connected with integrability
I. T. Habibullin, M. N Kuznetsova
In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call th…
On the recursion operators for integrable equations
I. T. Habibullin, A. R. Khakimova
It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symme…
On a direct algorithm for constructing recursion operators and Lax pairs for integrable models
I. T. Habibullin, A. R. Khakimova
We suggested an algorithm for searching the recursion operators for nonlinear integrable equations. It was observed that the recursion operator can be represented as a ratio of…
On a method for constructing the Lax pairs for nonlinear integrable equations
I. T. Habibullin, A. R. Khakimova, M. N. Poptsova
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax…
Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems
I. T. Habibullin, M. N. Poptsova
A method of the formal diagonalization of the discrete linear operator with a parameter is studied. In the case when the operator provides a Lax operator for a nonlinear quad syste…