On solution of Schrödinger–Hirota equation with Kerr law via Lie symmetry reduction

ÖNDER İ., SEÇER A., Hashemi M. S., ÖZIŞIK M., Bayram M.

Nonlinear Dynamics, vol.111, no.20, pp.19315-19327, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 111 Issue: 20
  • Publication Date: 2023
  • Doi Number: 10.1007/s11071-023-08879-9
  • Journal Name: Nonlinear Dynamics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.19315-19327
  • Keywords: Infinitesimal generators, Lie symmetry method, Prolongation, Riccati equation expansion method, Soliton solution
  • Yıldız Technical University Affiliated: Yes


In this study, we investigated Schrödinger–Hirota equation Kerr law in the presence of spatio-temporal dispersion which describes pulse propagation in optical fibers provoked by nonlinear effect and reduced to multi-plane dispersion. We used the Lie symmetry method to reduce the model into the nonlinear ordinary differential equations. Moreover, the unified Riccati equation expansion method was used to obtain optical soliton solutions and other soliton solutions of the model. We obtained dark, kink, singular, and periodic-singular soliton solutions. Obtained results were shown via 3D and contour graphs. Thus, the model was analyzed for the first time with the Lie symmetry method and UREEM.