Analytical and semi-analytical ample solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term

Abstract

In this paper, we investigate distinct novel analytical and semi-analytical solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term by the employment of there different schemes. These schemes are the generalized auxiliary equation method, the generalized exp--ϕξ expansion method, and the Adomain decomposition method that are considered as useful tools in this field. The suggested model in this study is used to explore the dynamics of light pulses for sub-10-fs-pulse propagation in the framework of computational simulations. The primary research of our study focuses on the case where the carrier wavelength of the soliton is much shorter than the spatial width. Herewith, the soliton frequency is smaller than the carrier frequency. The shorter femtosecond pulses (<100fs) is desired to increase the bit rate of pulse propagation. Their loss for the short-wavelength pulses that are propagating through the wave-guide is negligible. New analytical solutions are obtained, then it used to evaluate the initial and boundary conditions that are used in calculating the semi-analytical. Moreover, the accuracy of obtained solutions is explained by evaluating the absolute value of error between the obtained analytical and semi-analytical.

Keywords

• Sub-10-fs-pulse propagation
• Higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term
• Analytical and approximate solutions