43 citations · 108 across the 9 of their papers we have counts for
9 papers
Soliton Fay identities. I. Dark soliton case
V. E. Vekslerchik
We derive a set of bilinear identities for the determinants of the matrices that have been used to construct the dark soliton solutions for various models. To give examples of the…
Functional representation of the negative DNLS hierarchy
V. E. Vekslerchik
This paper is devoted to the negative flows of the derivative nonlinear Schrödinger hierarchy (DNLSH). The main result of this work is the functional representation of the extended…
Two-Dimensional Toda-Heisenberg Lattice
Vadim E. Vekslerchik
We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach,…
Bäcklund transformations between the AKNS and DNLS hierarchies
V. E. Vekslerchik
Starting from the functional representation of the Ablowitz-Kaup-Newell-Segur (AKNS) and derivative nonlinear Schrödinger (DNLS) hierarchies and using the chains of the Miura-like…
KdV-Volterra chain
G. M. Pritula, V. E. Vekslerchik
This paper is devoted to the system of coupled KdV-like equations. It is shown that this apparently non-integrable system possesses an integrable reduction which is closely related…
Backlund transformations for the Nizhnik-Novikov-Veselov equation
V. E. Vekslerchik
The Backlund transformations for the Nizhnik-Novikov-Veselov equation are presented. It is shown that these transformations can be iterated and that the resulting sequence can be d…
Stationary structures in two-dimensional continuous Heisenberg ferromagnetic spin system
G. M. Pritula, V. E. Vekslerchik
Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2+1)-dimensional Landau-Lifshitz…
Functional representation of the Ablowitz-Ladik hierarchy. II
V. E. Vekslerchik
In this paper I continue studies of the functional representation of the Ablowitz-Ladik hierarchy (ALH). Using formal series solutions of the zero-curvature condition I rederive th…
Functional representation of the Ablowitz-Ladik hierarchy
V. E. Vekslerchik
The Ablowitz-Ladik hierarchy (ALH) is considered in the framework of the inverse scattering approach. After establishing the structure of solutions of the auxiliary linear problems…