Bifurcations and dispersive optical solitons for the cubic-quartic nonlinear Lakshmanan-Porsezian-Daniel equation in polarization-preserving fibers

The main attention of this work is to study the bifurcations and optical solitons for the cubic- quartic nonlinear Lakshmanan-Porsezian-Daniel equation in polarization-preserving fibers. Firstly, the NLLPD equation was converted into an equivalent ordinary differential traveling wave system by using the traveling wave transformations. Then, we derive the system's Hamiltonian and orbits phase portraits. In addition to, we construct dark and singular solitons of this model by using the bifurcation theory of dynamical system method. As you can see, some other dispersive optical solitons have been deduced via the complete discriminant system technique and symbolic computation. It is notable that we give the classification of single traveling wave solutions for NLLPD model at the same time. The obtained conclusions may improve or complement previous conditions. Lastly, in order to further explore the propagation of NLLPD model in nonlinear optics, two-dimensional and three-dimensional graphs are drawn by selecting appropriate parameters of the optical soliton solutions.

Automated summary

This study focuses on investigating bifurcations and optical solitons for the cubic-quartic nonlinear Lakshmanan-Porsezian-Daniel equation in polarization-preserving fibers. Various methods such as traveling wave transformations, bifurcation theory of dynamical systems, and symbolic computation were utilized to derive dark solitons, singular solitons, and dispersive optical solitons, as well as classify single traveling wave solutions for the NLLPD model. Furthermore, two-dimensional and three-dimensional graphs were generated to explore the propagation of the NLLPD model in nonlinear optics.