Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics

Abstract

This article studies dark, bright, trigonometric and rational optical soliton solutions to the perturbed nonlinear Schrödinger–Hirota equation (PNLSHE). Hence, we have examined two cases: first, restrictions have been done to the third-order (TOD) (γ) as constraint relation, and the coupling coefficients (σ) is obtained as well as the velocity of the soliton by adopting the traveling wave hypothesis. Second, the TOD and the coupling coefficients are non-zero value, sending back to the PNLSHE, which has been studied in refs. [4,10,16] recently. By employing two relevant integration technics such as the auxiliary equation and the modified auxiliary equation method, miscellaneous optical solitary wave is obtianed, which is in agreement with the outcomes collected by the previous studies [4,16]. These results help in obtaining nonlinear optical fibers in the future.

Exact Soliton Solutions for Nonlinear Perturbed Schrödinger Equations with Nonlinear Optical Media

“…Many authors have introduced the definition of q-deformed hyperbolic functions (see, for example, [7,[12][13][14]). The q-deformed hyperbolic functions are defined by sinh q (ξ) = 1 2 (e ξ − qe −ξ ), and cosh q (ξ) = 1 2 (e ξ + qe −ξ ).…”

“…Many authors have defined the q-deformed trigonometric functions in [7,[12][13][14]26] as sin q (ξ) = 1 2i (e iξ − qe −iξ ), and cos q (ξ) = 1 2 (e iξ + qe −iξ ). In the q-deformed trigonometric functions methods, we suppose the solution of Equation ( 14) in the following form: Type 3.…”

“…The optical pulses in the optical solutions play a significant role in communication systems, optical fibers, and so on. Many authors have discussed the optical solutions for the nonlinear Schrödinger equation (NSE) when the nonlinear terms are Kerr law, power law, parabolic law, dual-power law, saturating law, exponential law, higher order polynomial law, and triple-power law (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). There are several previous studies which are of great interest in the optical solitons (see [18][19][20][21][22]).…”

Miscellaneous optical solitons in magneto-optic waveguides associated to the influence of the cross-phase modulation in instability spectra

“…Special attention has been also paid to magneto-optic waveguides in recent days. It has been underscore that it presents specificities compared to waveguides of other dielectric materials [8,9,13]. The study of optical solitons in magneto-optic waveguides is strongly consolidated by the results which indicate that waveguides reduce the phenomenon associated with soliton disorder, losses and a virtual reduction of the famous cross-talk.…”

“…Studies done these days in the magneto-optic wavesguides are based on mathematical models with various nonlinearities such as kerr nonlinearity, power-law nonlinearity, parabolic-law nonlinearity and dual powerlaw nonlinearity in the presence of the coefficients of self-phase modulation, nonlinear dispersion, Raman effect and many others [8,9]. The particularity of the model, which has been the subject of an investigation in [8,9,13], lies in the fact that the coupling coefficient with the neighbour is taken into account as well as the XPM coefficients.…”