Bifurcation, phase plane analysis and exact soliton solutions in the nonlinear Schrodinger equation with Atangana's conformable derivative


Alam M. N., Iqbal M., Hassan M., Fayz-Al-Asad M., Hossain M. S., Tunç C.

Chaos, Solitons and Fractals, vol.182, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 182
  • Publication Date: 2024
  • Doi Number: 10.1016/j.chaos.2024.114724
  • Journal Name: Chaos, Solitons and Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Keywords: Atangana's conformable fractional derivative, Bifurcation, Closed-form wave solutions, Hamiltonian, The modified (G′/G)-expansion method, The nonlinear Schrodinger equation
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

The nonlinear Schrodinger equation (NLSE) with Atangana's conformable fractional derivative (ACFD) is an equation that describes how the quantum state of a physical system changes in time. This present study examines the exact soliton results (ESRs) and analyze their bifurcations and phase plane (PP) of the NLSE with ACFD through the modified (G′/G)-expansion scheme (MG′/GES). Firstly, ACFD and its properties are included and then by MG′/GES, the exact soliton results and analyze their bifurcations and phase plane of NLSE, displayed with the ACFD, are classified. These obtained ESRs include periodic wave pulse, bright-dark periodic wave pulse, multiple bright-dark soliton pulse, and so many types. We provide 2-D, 3-D and contour diagrams, Hamiltonian function (HF) for phase plane dynamics analysis and bifurcation analysis diagrams to examine the nonlinear effects and the impact of fractional and time parameters on these obtained ESRs. The obtained ESRs illustration the novelty and prominence of the dynamical construction and promulgation performance of the resultant equation and also have practical effects for real world problems. The ESRs obtained with MG′/GES show that this scheme is very humble, well-organized and can be implemented to other the NLSE with ACFD.