Article citationsMore>>

Schürmann, H.W. and Serov, V.S. (2019) Guided TE-Waves in a Slab Structure with Lossless Cubic Nonlinear Dielectric and Magnetic Material: Parameter Dependence and Power Flow with Focus on Metamaterials. The European Physical Journal D, 73, Article No. 204.
https://doi.org/10.1140/epjd/e2019-100258-y

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.