12 citations · 62 across the 15 of their papers we have counts for
15 papers
Solitons of the constrained Schrödinger equations
V. E. Vekslerchik
We consider the linear vector Schrödinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik h…
Dark solitons of the Gross-Neveu model
V. E. Vekslerchik
We present N-soliton solutions for the classical (1+1)-dimensional Gross-Neveu model which satisfy non-zero boundary conditions. These solutions are obtained by direct method using…
Solitons of Some Nonlinear Sigma-Like Models
V. E. Vekslerchik
We present a set of differential identities for some class of matrices. These identities are used to derive the -soliton solutions for the Pohlmeyer nonlinear sigma-model, two-d…
Solitons of the vector KdV and Yamilov lattices
V. E. Vekslerchik
We study a vector generalizations of the lattice KdV equation and one of the simplest Yamilov equations. We use algebraic properties of a certain class of matrices to derive the N-…
Solitons of the (2+2)-dimensional Toda lattice
V. E. Vekslerchik
We use the generalized Cauchy matrix approach to derive the N-soliton solutions for the (2+2)-dimensional Toda lattice.
Solitons of a simple nonlinear model on the cubic lattice
V. E. Vekslerchik
We study a simple nonlinear model defined on the cubic lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely rel…