Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

Abstract

Nonlinear waves on periodic backgrounds play an important role in physical systems. In this study, nonlinear waves that include solitons, breathers, rogue waves, and semi-rational solutions on periodic backgrounds for the coupled Lakshmanan-Porsezian-Daniel equations are investigated. Moreover, the interactions between different types of nonlinear waves are examined and their dynamic behaviors are studied. In particular, it is observed that bright-dark rogue waves interact with bright-dark breathers or solitons on periodic backgrounds, four-petaled breathers interact with two eye-shaped breathers on periodic backgrounds, and a four-petal rogue wave interplays with a rogue wave on periodic backgrounds. Furthermore, it is found that the value of the parameter 𝜸 3 affects the weak and strong interactions of these nonlinear waves. These results may be useful in the study of nonlinear wave dynamics in coupled nonlinear wave models.

Semi-Analytical Closed-Form Solutions for Dynamical Rössler-Type System

“…Table 1. Values of the absolute errors: ϵ u = |u numerical − ūOPIM | for initial conditions x 0 = 0.25, y 0 = 0.75 and z 0 = 1.05 and different values of the index N max ; ūOPIM analytic approximate solution of Equation ( 8) obtained from Equations ( 37), (38) From Table 1, it can be observed that when the N max index increases, the magnitude of the absolute errors then decreases, until 10 −7 .…”

“…Table 2. The approximate analytic solution ūOPIM of Equation ( 8) given by Equations ( 37) and (38) and the corresponding numerical solution for initial conditions x 0 = 0.25, y 0 = 0.75, z 0 = 1.05 and the index N max = 30 (absolute errors:…”

“…Nonlinear wave dynamics, such as solitons, breathers, rogue waves and semi-rational solutions on periodic backgrounds, which are important for many physical systems, were investigated by Li et al [38], who pointed out their dynamic behaviors.…”

Cosine-Gaussian breathers controlled by the initial conditions in highly nonlocal media

“…The study of optical solitons has been a central theme in nonlinear optics, consistently revealing captivating phenomena and applications [1,2,3,4,5]. These solitons, especially when interacting with highly nonlocal media, present a myriad of intriguing behaviors.…”

Cosine-Gaussian breathers controlled by the initial conditions in highly nonlocal media

“…The study of optical solitons has been a central theme in nonlinear optics, consistently revealing captivating phenomena and applications [1,2,3,4,5]. These solitons, especially when interacting with highly nonlocal media, present a myriad of intriguing behaviors.…”