Phase portrait, bifurcation, chaotic pattern and optical soliton solutions of the Fokas-Lenells equation with cubic-quartic dispersion in optical fibers. (English) Zbl 1520.81083
Summary: The main purpose of this paper is to study the Fokas-Lenells equation with cubic-quartic dispersion describing the propagation of birefringent fibers and polarization preserving fibers. Firstly, using traveling wave transformation and homogeneous balance principle, the Fokas-Lenells equation with cubic-quartic dispersion is simplified into ordinary differential equation. Secondly, the dynamic properties of two-dimensional system and its perturbed system are studied. Finally, by using the trial method of polynomial of rank homogeneous equation, the optical soliton solutions of the Fokas-Lenells equation with cubic-quartic dispersion can be obtained. Moreover, three-dimensional diagram, two-dimensional diagram, density plot and contour plot of the obtained solutions are drawn by explaining the propagation of optical solitons.
MSC:
| 81Q50 | Quantum chaos |
| 81V80 | Quantum optics |
| 35C08 | Soliton solutions |
| 32L81 | Applications of holomorphic fiber spaces to the sciences |
| 81U30 | Dispersion theory, dispersion relations arising in quantum theory |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
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