Crank-Nicolson Scheme for Solving the Modified Nonlinear Schrodinger Equation

Abstract

Purpose The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme. Design/methodology/approach The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities. Findings The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients. Originality/value The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.

Guest editorial

“…After comprehensive peer review, only one third papers qualified for acceptance for final publication. This special issue comprises the theoretical and experimental research articles that elucidate the research efforts and recent developments on “New Trends in Heat and Fluid Flow: Applications and Recent Developments.” This issue consists of (Agrawal et al , 2021; Akbari et al , 2021; Alanazi et al , 2021; Alkanhal, 2021; Chang et al , 2021; Chen et al , 2021; Dehghan et al , 2021; Hayat et al , 2021; Riaz et al , 2021; Saadun et al , 2021; Safdari Shadloo, 2020; Selimefendigil and Öztop, 2021; Ullah et al , 2021; Xing et al , 2021; Yilmaz, 2021; Youjun et al , 2020; Zaher et al , 2021; Zhang et al , 2020) accepted papers related to fluid dynamics; heat exchangers; heat transfer enhancement; heat and mass transfer in thermal energy; heat and mass transfer in porous media; heat transfer phenomena in biological systems; nanofluids; two-phase/multiphase flows; Newtonian and non-Newtonian fluids; thermodynamics; and numerical simulations and methods. The presented results are discussed with an adequate physical interpretation.…”

Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

“…The method is constrained by Robin and Dirichlet boundary conditions and has sufficient conditions for the oscillation of differential equation solutions, which can realize the oscillation analysis of nonlinear differential equation solutions. Reference [11] studied the complex dynamic behavior of a new type of chaotic system and introduced a memristor. Based on eigenvalue theory, the stability of a memristor system is analyzed by selecting a key parameter.…”