7 research outputs found
Perturbation theory for the modified nonlinear Schr{\"o}dinger solitons
The perturbation theory based on the Riemann-Hilbert problem is developed for
the modified nonlinear Schr{\"o}dinger equation which describes the propagation
of femtosecond optical pulses in nonlinear single-mode optical fibers. A
detailed analysis of the adiabatic approximation to perturbation-induced
evolution of the soliton parameters is given. The linear perturbation and the
Raman gain are considered as examples.Comment: 22 pages, Latex, no figures. Submitted to Physica
Perturbation-induced radiation by the Ablowitz-Ladik soliton
An efficient formalism is elaborated to analytically describe dynamics of the
Ablowitz-Ladik soliton in the presence of perturbations. This formalism is
based on using the Riemann-Hilbert problem and provides the means of
calculating evolution of the discrete soliton parameters, as well as shape
distortion and perturbation-induced radiation effects. As an example, soliton
characteristics are calculated for linear damping and quintic perturbations.Comment: 13 pages, 4 figures, Phys. Rev. E (in press
Doubly periodic waves of a discrete nonlinear Schr\"odinger system with saturable nonlinearity
A system of two discrete nonlinear Schr\"odinger equations of the
Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly
periodic wave, whose long wave limit is also derived. As a by-product, several
new solutions of the elliptic type are provided for NLS-type discrete and
continuous systems.Comment: 12 pages, to appear, Journal of nonlinear mathematical physic