Dissipative structures in the resonant interaction of laser radiation with nonlinear dispersive medium

Abstract

The article presents the results of studies on the stability of dissipative structures (DS) arising in the resonant interaction of laser radiation with a nonlinear medium. Resonant interaction is modeled by the one dimensional complex Ginzburg-Landau equation with a nonconservative cubic–quintic nonlinearity. The areas of existence of stable DS solutions have been determined analytically using a variational approach and confirmed numerically by extensive numerical simulations.

A Semiclassical Approach to the Nonlocal Nonlinear Schrödinger Equation with a Non-Hermitian Term

“…Ψ (t, h) are given by (19). Let us present the operators V( ẑ, t), V( ẑ, t), W( ẑ, ŵ, t), and W( ẑ, ŵ, t) from (1) in the form of formal power series in ∆ ẑ and ∆ ŵ in a neighborhood of the trajectory z = Z(t).…”

“…The Lindblad master equation, which is also widely used for the study of open quantum systems, is derived from the microscopic dynamics [16,17] as opposed to the models under consideration that can be treated as macroscopic ones. The dissipative NLSE also arises in the description of solitons in nonlinear media such as the cavity of the mode-locked lasers (the so-called Haus master equation [18] that is the (1 + 1)-NLSE with a non-Hermitian term) and related models [19] including multidimensional [20] and nonlocal [21] ones.…”