Self-Focusing with Fourth-Order Dispersion

New types of stable nonlinear whistler waveguides

The stationary self-focusing of whistler waves with frequencies near half of the electron-cyclotron frequency in the ionospheric plasma is considered in the framework of a two-dimensional generalized nonlinear Schrödinger equation including fourth-order dispersion effects and nonlinearity saturation. New types of soliton-like (with zero topological charge) and vortex-like nonlinear waveguides a...

Impact of Fourth-Order Dispersion Coefficient on the Gain Spectrum and the Saturation Behavior of One-Pump Fiber Optical Parametric Amplifiers

In this paper, the gain spectrum and the saturation behavior of one-pump fiber optical parametric amplifiers (1-P FOPAs) are investigated by taking into account the fourth-order dispersion coefficient b4 in the analysis. The results show that it is necessary to consider b4 in the analysis when the wavelength difference between the signal and pump waves is large enough and/or whenever the pump w...

Fourth Order Time-stepping for Low Dispersion Korteweg-de Vries and Nonlinear Schrödinger Equations

Abstract. Purely dispersive equations, such as the Korteweg-de Vries and the nonlinear Schrödinger equations in the limit of small dispersion, have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral ...

für Mathematik in den Naturwissenschaften Leipzig Fourth order time - stepping for low dispersion

Purely dispersive equations as the Korteweg-de Vries and the nonlinear Schrödinger equation in the limit of small dispersion have solutions to Cauchy problems with smooth initial data which develop a zone of rapid modulated oscillations in the region where the corresponding dispersionless equations have shocks or blowup. Fourth order time-stepping in combination with spectral methods is benefic...

High-order Dispersion Effects in Self-focusing