Abstract. We consider a nonlinear Schrodinger equation (NLS) with dissipation and forcing in critical dimension. Without both linear and nonlinear dissipation NLS results in a flnite-time singularity (collapse) for any initial conditions. Dissipation ensures collapse regularization. If dissipation is small then multiple near-singular collapses are randomly distributed in space and time forming ...

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, th...

The modulational stability of the nonlinear Schrödinger (NLS) equation is examined in the cases with linear and quadratic external potential. This study is motivated by recent experimental studies in the context of matter waves in BoseEinstein condensates (BECs). The linear case can be examined by means of the Tappert transformation and can be mapped to the NLS in the appropriate (constant acce...

The modulational instability, a destabilization mechanism for plane waves, occurs ubiquitously in spatially extended dynamical systems arising in fluid dynamics, nonlinear optics, atomic physics, and other disciplines. In this paper, we investigate analytically, numerically, and experimentally the modulational instability in a layered cubically nonlinear (Kerr) optical medium that consists of a...

The present article represents part of the PhD. dissertation by C. Josserand1. We discuss the nucleation of quantized vortices in the nonlinear Schrödinger equation (NLS) for a flow around a disk in two spatial dimensions. It appears that the vortices are nucleated when the flow becomes locally (at the edge of the disk) supersonic. A detailed study of the phase equation for the complex field ψ ...

The main scope of this paper is to examine the smoke ring (or vortex filament) equation which can be viewed as a dynamical system on space curve in E³. differential geometric properties soliton surface accociated with Nonlinear Schrödinger (NLS) equation, called NLS or Hasimoto surface, are investigated by using Darboux frame. Moreover, Gaussian and mean curvature found terms curvatures k_{n}, ...

Nevus lipomatosus superficialis (NLS) is a hamartomatous skin lesion defined by the presence of mature adipose tissues among the collagen bundles of the dermis. It is classified into two forms:the classical form and the solitary form. The classical NLS most commonly involves the pelvic or gluteal region. In this paper, we report a case of classical NLS over the neck because of its atypica...

We consider reduced-order modeling of nonlinear dispersive waves described by a class Schrödinger (NLS) equations. compare two methods: (i) The reduced Lagrangian approach which relies on the variational formulation NLS and (ii) recently developed method solutions (RONS). First, we prove surprising result that, although methods are seemingly quite different, they can be obtained from real imagi...

The focusing cubic NLS is a canonical model for the propagation of laser beams. In dimensions 2 and 3, it is known that a large class of initial data leads to finite time blow-up. Now, physical experiments suggest that this blow-up does not always occur. This might be explained by the fact that some physical phenomena neglected by the standard NLS model become relevant at large intensities of t...