Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

The de Broglie Wavelength

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

Consider a wooden box and a cylinder of known masses m1 and m2, respectively, hanging from a ceiling with the help of a massless pulley system.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Low complexity neural network equalizer for nonlinearity mitigation in digital subcarrier multiplexing systems.

Optics express·2025

Same author

Experimental validation of XPM mitigation using a generalizable multi-task learning neural network.

Optics letters·2024

Same author

Channel model for the dual-polarization b-modulated nonlinear frequency-division multiplexing optical transmission systems.

Optics express·2023

Same author

Memory-aware end-to-end learning of channel distortions in optical coherent communications.

Optics express·2023

Same author

Attention-aided partial bidirectional RNN-based nonlinear equalizer in coherent optical systems.

Optics express·2022

Same author

Experimental implementation of a neural network optical channel equalizer in restricted hardware using pruning and quantization.

Scientific reports·2022

Search research articles

Related Experiment Video

Updated: Jun 28, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Random input problem for the nonlinear Schrödinger equation.

Stanislav A Derevyanko¹, Jaroslaw E Prilepsky

¹Photonics Research Group, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom. s.derevyanko@aston.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2008

Summary

This study analyzes soliton generation from random inputs in nonlinear systems using the nonlinear Schrödinger equation (NLSE). It provides insights into spectral density and minimal pulse width for soliton creation under different noise models.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Related Experiment Videos

Last Updated: Jun 28, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

Nonlinear Dynamics
Quantum Optics
Wave Propagation

Background:

The nonlinear Schrödinger equation (NLSE) models various wave phenomena.
Understanding soliton formation from random inputs is crucial for applications.

Purpose of the Study:

To investigate soliton creation from random inputs in a self-focusing NLSE.
To analyze the spectral density of waves generated by disordered input fields.
To determine the conditions for soliton generation from specific noise models.

Main Methods:

Direct scattering problem analysis for the NLSE.
Modeling random inputs using complex Gaussian white noise and a real dichotomous process.
Deriving closed-form expressions and perturbative expansions for spectral density.

Main Results:

Obtained closed-form expression for averaged spectral density for Gaussian white noise.
Derived a perturbative expansion for spectral density with dichotomous input.
Determined the distribution of minimal pulse width for soliton generation with dichotomous input.

Conclusions:

The study provides a theoretical framework for soliton generation from random inputs.
Results are applicable to nonlinear diffraction, fiber gratings, and optical fiber communications.
Offers quantitative predictions for soliton formation under realistic disordered conditions.