There exists a particular class of boundary value problems for integrable nonlinear evolution equations formulated on the half-line, called linearizable. For this problems, Fokas method yields formalism solution associated initial-boundary problem, which is as efficient analogous Cauchy problem. Here, we employ analysis several concrete Schrodinger equation. This includes involving initial cond...

We study the Cauchy problem for nonlinear Schrodinger equations with attractive inverse-power potentials. By using variational arguments, we first determine a sharp threshold of global well-posedness and blow-up equation in mass-supercritical case. next existence orbital stability standing waves mass-subcritical mass-critical cases. In case, give detailed description behavior when mass tends to...

Three-dimensional (3D) superflows past a circular cylinder are studied by numerically integrating the nonlinear Schrodinger equation. 3D initial data are built from the two-dimensional (2D) stationary vortex nucleation solutions. Quasistationary half-ring vortices, pinned at the sides of the cylinder, are generated after a short time. On a longer time scale, either 3D vortex stretching induces ...

Optical pulse compression using similariton propagation in an optical fibre with decreasing dispersion has been demonstrated for the first time. This scheme is a practical application of sech-similariton solution to generalized nonlinear schrodinger equation(NLSE) distributed coefficients recently found self similarity technique. The profile constructed comb-profile approximation technique and ...

Vortex motion in ordered structures is analysed numerically in the frame of the 2D nonlinear Schrodinger equation. ̈ Ž . Analogies with superfluid dynamics are presented. It was found that coherent interaction of optical vortex solitons OVSs leads to vortex motion, which can be adequately described by the Kelvin law in superfluid dynamics for large offsets between the OVSs. Cancelation of motion...

Self-compression of multi-millijoule femtosecond laser pulses and dramatic increase of the peak intensity are found in pressurized helium and neon within a range of intensity in which the ionization modification of the material parameters by the pulse is negligible. The pulse propagation is studied by the (3+1)-dimensional nonlinear Schrodinger equation including basic lowest order optical proc...

By numerically solving the nonlinear Schrodinger equation, we analyze pulse propagation through dispersion decreasing optical fibers (DDFs) in which the core radius varies along the length of the fiber; this in turn leads to a variation of dispersion as well as mode effective area along the length of the fiber. We calculate an optimum core radius profile required to create a local balance betwe...