• Corpus ID: 248506001

Fourier spectrum and related characteristics of the fundamental bright soliton solution

@inproceedings{Karjanto2022FourierSA,
  title={Fourier spectrum and related characteristics of the fundamental bright soliton solution},
  author={Natanael Karjanto},
  year={2022}
}
We derive exact analytical expressions for the spatial Fourier spectrum of the fundamental bright soliton solution for the ( 1 + 1 ) -dimensional nonlinear Schrödinger 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… 

Figures from this paper

References

SHOWING 1-10 OF 41 REFERENCES

On spatial Fourier spectrum of rogue wave breathers

In this article, we derive exact analytical expressions for the spatial Fourier spectrum of the soliton family on a constant background. Also known as breathers, these solitons are exact solutions of

Solitons and the Inverse Scattering Transform

Dispersion and nonlinearity play a fundamental role in wave motions in nature. The nonlinear shallow water equations that neglect dispersion altogether lead to breaking phenomena of the typical

Solitons : nonlinear pulses and beams

Basic equations. The nonlinear Schrodinger equation. Exact solutions. Non-Kerr-law nonlinearities. Normal dispersion regime. Multiple-port linear devices made from solitons. Nonlinear pulses in

The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation

A detailed analysis is given to the solution of the cubic Schrodinger equation iqt + qxx + 2|q|2q = 0 under the boundary conditions as |x|→∞. The inverse-scattering technique is used, and the

Formation of a Matter-Wave Bright Soliton

TLDR
The production of matter-wave solitons in an ultracold lithium-7 gas opens possibilities for future applications in coherent atom optics, atom interferometry, and atom transport.

The nonlinear Schrödinger equation : self-focusing and wave collapse

Basic Framework.- The Physical Context.- Structural Properties.- Rigorous Theory.- Existence and Long-Time Behavior.- Standing Wave Solutions.- Blowup Solutions.- Asymptotic Analysis near Collapse.-

Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media

It is demonstrated that the equation iol/J/ot + l/Jxx + K 1¢12 1/1 = 0, which describes plane self-focusing and one-dimensional self-modulation can be solved exactly by reducing it to the inverse

Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion

Theoretical calculations supported by numerical simulations show that utilization of the nonlinear dependence of the index of refraction on intensity makes possible the transmission of picosecond

Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers

This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger equation. These breathers belong to the family of solitons on a non-vanishing and constant

Application of Darboux Transformation to solve Multisoliton Solution on Non-linear Schr\

Darboux transformation is one of the methods used in solving nonlinear evolution equation. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the