A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation

A Modulation Method for Self-focusing in the Perturbed Critical Nonlinear Schr Odinger Equation

In this Letter we introduce a systematic perturbation method for analyzing the e ect of small perturbations on critical self focusing by reducing the perturbed critical nonlinear Schrodinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simpli ed, depending on whether PNLS is power conserving ...

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...

A Modulation Method for Self-focusing in the Perturbed

In this Letter we introduce a systematic perturbation method for analyzing the eeect of small perturbations on critical self focusing by reducing the perturbed critical nonlinear Schrr odinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simpliied, depending on whether PNLS is power conserving...

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.

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