Nonlinear Schrödinger equation including growth and damping

Abstract

The nonlinear Schrödinger equation, with complex coefficients that describe growth and damping, is considered. An exact stationary soliton solution is found for arbitrary growth and damping strength.

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

“…To this end, we consider a complex Ginzburg-Landau model with the cubic nonlinearity (CGL3), for which an analytical chirped-sech localized solution is well known in the one-dimensional (1D) setting [10,11]. While this solution is always unstable, it has been shown that an additional, linearly coupled, dissipative linear equation can lead to its stabilization in coupled-waveguide models, keeping the solution in the exact analytical form [8,12,13].…”

Dynamics of the transition from polarization disorder to antiphase polarization domains in vector fiber lasers

“…4 shows that, when operating in the BF unstable regime (i.e., we have set α = 0.6, β = 3, so that 1 − αβ < 0, ρ = −3, and γ = 0.95), it is also possible to generate a uniform and spatiotemporally stable lattice of anticorrelated (or antiphase) temporal solitons. The individual pulses in each polarization component are well matched by the exact soliton-like solution of the scalar complex GinzburgLandau equation [45], namely,…”

Role of dispersion in pulse emission from a sliding-frequency fiber laser

“…(1) are nonlinearity and bandwidthlimited amplification, irrespective of the sign of GVD. 14,15 Neglecting at first for simplicity higher-order nonlinear gain saturation and frequency shifting, that is, with s a 0, one obtains an exact solution for Eq. (1) in the form 11,14 u A͓sech͑T͞r͔͒ 12in exp͑iGZ͒ ,…”