Soliton turbulence in the complex Ginzburg-Landau equation

The Complex Ginzburg-landau Equation∗

Essential to the derivation of the Ginzburg-Landau equation is assumption that the spatial variables of the vector field U(x, y, t) are defined on a cylindrical domain. This means that (x, y) ∈ R ×Ω, where Ω ⊂ R is a open and bounded domain (and m ≥ 1, n ≥ 0), so that U : R ×Ω×R+ → R . The N ×N constant coefficient matrix Sμ is assumed to be non-negative, in the sense that all its eigenvalues a...

The Complex Ginzburg-Landau equation for beginners

Several systems discussed at this workshop on Spatio-Temporal Patterns in Nonequilibrium Complex Systems have been related to or analyzed in the context of the so-called Complex Ginzburg-Landau equation (CGL). What is the difference between the physics underlying the usual amplitude description for stationary patterns and the one underlying the CGL? Why are there many more stable coherent struc...

Analytical approximation of the soliton solutions of the quintic complex Ginzburg-Landau equation

We have performed a theoretical study of the soliton fiber laser based on the quintic complex GinzburgLandau equation ~CGLE!. This study may also apply to soliton propagation in telecommunications systems. We have developed a simple approach that allows us to obtain, in an approximate way, analytical expressions for the stable pulselike solutions of the CGLE. The method also gives an accurate e...

Diiusion and Weak Turbulence in Capillary Waves and in the Complex Ginzburg-landau Equation

Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation.

Soliton solutions of the one-dimensional (1D) complex Ginzburg-Landau equations (CGLE) are analyzed. %e have developed a simple approach that applies equally to both the cubic and the quintic CGLE. This approach allows us to find an extensive list of soliton solutions of the COLE, and to express all these solutions explicitly. In this way, we were able to classify them clearly. %'e have found a...