Fourier spectrum and related characteristics of the fundamental bright soliton solution

TL;DR

This paper derives exact Fourier spectrum expressions for the fundamental bright soliton in the nonlinear Schrödinger equation, confirming key spectral properties and highlighting its applications in fiber optics and telecommunications.

Contribution

It provides analytical Fourier spectrum formulas for the fundamental bright soliton, demonstrating shape-preserving properties and confirming key spectral relations.

Findings

Fourier spectrum expressions are exact and shape-preserving.

Fundamental soliton satisfies Parseval's relation.

Satisfies stretch-bandwidth reciprocity.

Abstract

We derive exact analytical expressions for the spatial Fourier spectrum of the fundamental bright soliton solution for the $(1 + 1)$-dimensional nonlinear Schr\"odinger equation. Similar to a Gaussian profile, the Fourier transform for the hyperbolic secant shape is also shape-preserving. We further confirm that the fundamental soliton indeed satisfies essential characteristics such as Parseval's relation and the stretch-bandwidth reciprocity relationship. The fundamental bright solitons find rich applications in nonlinear fiber optics and optical telecommunication systems.