Self-focusing in the Complex Ginzburg-landau Limit of the Critical Nonlinear Schrr Odinger Equation

Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...

Exact solutions of the 2D Ginzburg-Landau equation by the first integral method

The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.

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

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...

Dissipation at Singularities of the Nonlinear Schrr Odinger Equation through Limits of Regularisations

The possibility of physically relevant singular solutions of the nonlinear Schrr odinger equation (NLSE) with sustained dissipation into the singularity is considered through numerical study of a dissipative regularisation and its small dissipation limit. A new form of such dissipative solutions is conjectured for certain parameter ranges where this behaviour was previously not expected, involv...