Intensity variability in stationary solutions of the Fractional Nonlinear Schrödinger Equation

¹ Department of Mathematics, Universitas Syiah Kuala, Banda Aceh, Indonesia
² Department of Informatics, Universitas Syiah Kuala, Banda Aceh, Indonesia
³ Mathematics Graduate Program, Universitas Syiah Kuala, Banda Aceh, Indonesia

^* Corresponding author: marwan.math@usk.ac.id

Abstract

Solitons that propagate in optical fiber with indexes of refraction, dispersion, and diffraction are balanced, making pulses or electromagnetic waves propagate without any distortion. This is closely related to use of nonlinear refractive index in fiber optics. If an optical fiber only uses a nonlinear refractive index, then the partial signal can be lost over time. This study aims to analyze the variability of stationary solutions in multi-solitons formed using Fractional Nonlinear Schrödinger (FNLS). The parameter p indicates energy level of the solution to FNLS equation which has a positive integer value. This study focuses on 3 variations of p values, namely p = 0 which indicates the ground state, p = 1 which indicates the first excited state, and p = 2 which indicates the second excited state. During the first to second excited state, multi soliton peaks are formed with the same amplitude symmetrically. The amplitude experienced by the middle soliton in second excited state is lower which indicates the input signal obtained from the FNLS solution in the ground state in the form of triple-soliton. The polarization mode cause the soliton pulse width to shrink and the consequent amplitude in the first excited state to increase.