Related Experiment Video
Updated: May 26, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Front and pulse solutions for the complex Ginzburg-Landau equation with higher-order terms
Huiping Tian1, Zhonghao Li, Jinping Tian
1Department of Electronics and Information Technology, Shanxi University, Taiyuan, People's Republic of China. tianhuip@mail.sxu.edu.cn
Abstract:
We investigate one-dimensional complex Ginzburg-Landau equation with higher-order terms and discuss their influences on the multiplicity of solutions. An exact analytic front solution is presented. By stability analysis for the original partial differential equation, we derive its necessary stability condition for amplitude perturbations. This condition together with the exact front solution determine the region of parameter space where the uniformly translating front solution can exist. In addition, stable pulses, chaotic pulses, and attenuation pulses appear generally if the parameters are out of the range. Finally, applying these analysis into the optical transmission system numerically we find that the stable transmission of optical pulses can be achieved if the parameters are appropriately chosen.
Related Concept Videos
Poisson's And Laplace's Equation
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Second Order systems II
If ζ...
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Separable Differential Equations
Differential Equations: Problem Solving

