Effective dispersion in the focusing nonlinear Schrödinger equation

Self-Focusing in the Damped Nonlinear Schrödinger Equation

We analyze the effect of damping (absorption) on critical self-focusing. We identify a threshold value δth for the damping parameter δ such that when δ > δth damping arrests blowup. When δ < δth, the solution blows up at the same asymptotic rate as the undamped nonlinear Schrödinger equation.

Effective noise theory for the nonlinear Schrödinger equation with disorder.

For the nonlinear Shrödinger equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear term acts as random noise. In the present work, the properties of this effective noise are studied numerically. Some assumptions made in earlier work were veri...

Self-focusing in the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger equation

Self-Focusing in the Perturbed and Unperturbed Nonlinear Schrödinger Equation in Critical Dimension

The formation of singularities of self-focusing solutions of the nonlinear Schrodinger equation (NLS) in critical dimension is characterized by a delicate balance between the focusing nonlinearity and di raction (Laplacian), and is thus very sensitive to small perturbations. In this paper we introduce a systematic perturbation theory for analyzing the e ect of additional small terms on self fo...

Integrable nonlocal nonlinear Schrödinger equation.

A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contras...