Rogue waves of the Fokas-Lenells equation

The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in the leading asymptotic order the nonlinear Schr\"odinger (NLS) equation results). Here we present an explicit analytical representation for the rogue waves of the FL equation. This representation is constructed by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution. when certain higher-order nonlinear effects are considered, the propagation of rogue waves in optical fibers is given.Comment: 7 pages, 3 figure

Study of implosion in an attractive Bose-Einstein condensate

By solving the Gross-Pitaevskii equation analytically and numerically, we reexamine the implosion phenomena that occur beyond the critical value of the number of atoms of an attractive Bose-Einstein condensate (BEC) with cigar-shape trapping geometry. We theoretically calculate the critical number of atoms in the condensate by using Ritz's variational optimization technique and investigate the stability and collapse dynamics of the attractive BEC by numerically solving the time dependent Gross-Pitavskii equation