Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber

Abstract

In this paper, the generalized second-order nonlinear Schrödinger equation with light-wave promulgation in an optical fiber, is studied for optical soliton solutions. Three analytical methods such as the $\mathrm{exp}\left(-\phi \left(\chi \right)\right)$-expansion method, the G′/G2-expansion method and the first integral methods are used to extract dark, singular, periodic, dark-singular combo optical solitons for the proposed model. These solitons appear with constraint conditions on their parameters and they are also presented. These three strategic schemes have made this retrieval successful. The given model is also studied for modulation instability on the basis of linear stability analysis. A dispersion relation is obtained between wave number and frequency.

Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis

“…Linear stability analysis (LSA) is the cornerstone of modulation instability (MI) analysis. An investigation of modulation stability [ 3 ] of the DNA Peyrard-Bishop model has been conducted in this paper. A perturbed steady-state solution of the model is assumed, as where incident power is represented by Z 0 and Γ( x , t ) is denoting the perturbation term.…”

“…The nonlinear evolution equations are the key to examine and analyze problems found in numerous fields like biology, zoology, physics, chemistry, optics, fluid mechanics and geophysics. A variety of nonlinear models are investigated by different researchers like nonlinear Schrödinger equation [ 1 – 3 ], geophysical Korteweg-de Vries equation [ 4 ], Ablowitz-Kaup-Newell-Segur equation [ 5 ], (3 + 1)sine-Gordon equation [ 6 ] and many other equations. Various models are examined in detail for deriving soliton solutions [ 7 – 10 ].…”

Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity

“…In addition, NLSEs play an important role in optic branch of physics. Optical simulation of gravity effect [11] , Kerr effect [12] , dark shock waves [13] , chaotic behavior of NLSE system [14] , solitons in thermo-optical media [15] , femtosecond behavior in optical waveguide [16] , stability analysis of optical solitons [17] , dynamics of solitons [18] , Bragg gratings [19] and much more can be cited as examples [20] , [21] , [22] , [23] .…”

Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

“…The importance of optical solitons for fundamental studies and technological applications in Photonic and Optics, such as bio-optical devices, all-optical switching, ultrafast communication systems, telecommunication engineering and all-optical gates is well known [9], [10], [11], [12], [13], [14]. The nonlinear Schrodinger equation (NLSE) is considered to be the key model to describes the dynamics of propagation of light-wave in an optical fiber [15], [16], [17], [18]. In the past few decades, many mathematician and scientist developed a powerful and direct techniques for the construction of analytical solutions of nonlinear evolution equations [19], [20], [21], [22].…”