Analytical soliton solutions of the higher order cubic-quintic nonlinear Schrödinger equation and the influence of the model's parameters


ESEN H., SEÇER A., ÖZIŞIK M., Bayram M.

Journal of Applied Physics, vol.132, no.5, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 132 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1063/5.0100433
  • Journal Name: Journal of Applied Physics
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Chemical Abstracts Core, Compendex, Computer & Applied Sciences, INSPEC, zbMATH

Abstract

© 2022 Author(s).In this paper, we present the higher-order nonlinear Schrödinger equation (NLSE) with third order dispersion (3OD), fourth-order dispersion (4OD), and cubic-quintic nonlinearity (CQNL) terms that define the propagation of ultrashort pulses. Two analytical methods, which are the new Kudryashov's method and the unified Riccati equation expansion method, are implemented to extract the analytical soliton solutions of the presented equation for the first time. Thus, bright, dark, and singular soliton solutions are acquired. To illustrate the physical behavior of some of the obtained solutions, 3D, 2D, and contour graphs are depicted. In particular, to understand the effects of the group velocity dispersion, 3OD, 4OD, CQNLs, self-steepening coefficient terms, and group velocity term of the traveling wave transformation on the soliton dynamics of the proposed equation, 2D plots for different values of coefficients are represented. The obtained results provide us with the knowledge that the presented model can be examined from a physical perspective. It can be concluded that the used methods are effective approaches to derive the analytical solutions for the NLSE.