TITLE:
Traveling Wave Solutions of the Quintic Complex One-Dimensional Ginzburg-Landau Equation
AUTHORS:
Hans Werner Schürmann, Valery Serov
KEYWORDS:
Ginzburg-Landau Equation, Weierstrass’ Elliptic Function, Phase Diagram
JOURNAL NAME:
Applied Mathematics,
Vol.12 No.7,
July
16,
2021
ABSTRACT: A subset of traveling wave solutions of the quintic complex Ginzburg-Landau equation (QCGLE) is presented in compact form. The approach consists of the following parts: 1) Reduction of the QCGLE to a system of two ordinary differential equations (ODEs) by a traveling wave ansatz; 2) Solution of the system for two (ad hoc) cases relating phase and amplitude; 3) Presentation of the solution for both cases in compact form; 4) Presentation of constraints for bounded and for singular positive solutions by analysing the analytical properties of the solution by means of a phase diagram approach. The results are exemplified numerically.