Article citationsMore>>

(a) Musette, M. and Conte, R. (2003) Analytic Solitary Waves of Nonintegrable Systems. Physica D: Nonlinear Phenomena, 181, 70-79. (Preprint nlin.PS/0302051)
https://doi.org/10.1016/S0167-2789(03)00069-1 (b) Conte, R. and Musette, M. (2009) Elliptic General Analytic Solutions. Studies in Applied Mathematics, 123, 63-81.
https://doi.org/10.1111/j.1467-9590.2009.00447.x

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.