30 research outputs found
Existence threshold for the ac-driven damped nonlinear Schr\"odinger solitons
It has been known for some time that solitons of the externally driven,
damped nonlinear Schr\"odinger equation can only exist if the driver's
strength, , exceeds approximately , where is the
dissipation coefficient. Although this perturbative result was expected to be
correct only to the leading order in , recent studies have demonstrated
that the formula gives a remarkably accurate
description of the soliton's existence threshold prompting suggestions that it
is, in fact, exact. In this note we evaluate the next order in the expansion of
showing that the actual reason for this phenomenon is simply
that the next-order coefficient is anomalously small: . Our approach is based on a singular perturbation expansion
of the soliton near the turning point; it allows to evaluate
to all orders in and can be easily reformulated for other perturbed
soliton equations.Comment: 8 pages in RevTeX; 5 figures in ps format included in the text. To be
published in Physica
Emission of Two Hard Photons in Large-Angle Bhabha Scattering
A closed expression for the differential cross section of the large-angle
Bhabha scattering which explicitly takes into account the leading and
next-to-leading contributions due to the emission of two hard photons is
presented. Both collinear and semi-collinear kinematical regions are
considered. The results are illustrated by numerical calculations.Comment: 13 pages, LaTeX, 1 PostScript figure, submitted to Nucl. Phys.