1 citations · 1 across the 2 of their papers we have counts for
6 papers
Soliton generation of two-component Bose-Einstein condensates in optical lattices
N. A. Kostov, V. Z. Enol'skii, V. S. Gerdjikov +2
Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trappe…
Algebraic and Analytic Aspects of Soliton Type Equations
Vladimir S. Gerdjikov
This is a review of two of the fundamental tools for analysis of soliton equations: i) the algebraic ones based on Kac-Moody algebras, their central extensions and their dual algeb…
Dynamical models of adiabatic -soliton interactions
V. S. Gerdjikov
The adiabatic N-soliton train interactions for the scalar nonlinear Schrodinger (NLS) equation and its perturbed versions are well studied. Here we briefly outline how they can be…
Reductions and real forms of Hamiltonian systems related to N-wave type equations
V. S. Gerdjikov, G. G. Grahovski
Reductions of N-wave type equations related to simple Lie algebras and the hierarchy of their Hamiltonian structures are studied. The reduction group G_R is realized as a subgroup…
N-soliton train interactions and perturbed complex Toda chain in nonlinear optics. Adiabatic and non-adiabtic aspects
V. S. Gerdjikov, I. M. Uzunov
Our previous results on the N-soliton interaction in the adiabatic approximation have been extended. It is shown that the complex Toda chain (CTC) model is an universal one in the…
Nonlinear waves, differential resultant, computer algebra and completely integrable dynamical systems
N. A. Kostov, Z. T. Kostova
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equa…