Degenerate elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation
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. - Reduction of the QCGLE to a system of two ordinary differential equations (ODEs) by a traveling wave ansatz. - Solution of the system for two (ad hoc) cases relating phase and amplitude. - Presentation of the solution for both cases in compact form. - Presentation of constraints for bounded and for singular positive solutions by analyzing the analytical properties of the solution by means of a phase diagram approach. The results are exemplified numerically
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.