Article citationsMore>>

Conte, R. and Musette, M. (2005) Solitary Waves of Nonlinear Nonintegrable Equations. In: Akhmediev, N.N. and Ankiewicz, A., Eds., Dissipative Solitons, Vol. 661, Springer, Berlin, 373-406. (Preprint nlin.PS/0407026)
https://doi.org/10.1007/10928028_15

has been cited by the following article:

• 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.