Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

42.3K
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.
42.3K
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

1.1K
Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations:...
1.1K
Graphing the Wave Function01:13

Graphing the Wave Function

1.8K
Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
1.8K
Equations of Wave Motion01:02

Equations of Wave Motion

5.8K
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
5.8K
The de Broglie Wavelength02:32

The de Broglie Wavelength

25.9K
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...
25.9K
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

4.0K
A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time....
4.0K

You might also read

Related Articles

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

Sort by
Same journal

Dynamical thermalization and turbulence in social stratification models.

Chaos (Woodbury, N.Y.)·2026
Same journal

Endogenous regime switching driven by scalar-irreducible learning dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

The coherence analysis and Laplacian spectrum applications of cycle-based iterative networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Hitting times, recurrence, and local dimension under nonstationary forcing with applications to climate data.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multiscale deep reservoir computing for predicting chaotic dynamical systems.

Chaos (Woodbury, N.Y.)·2026
Same journal

Chaotic decoherence under finite resolution: Lyapunov-controlled interference suppression.

Chaos (Woodbury, N.Y.)·2026

Related Experiment Video

Updated: Jun 29, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.0K

Rogue wave pattern of multi-component derivative nonlinear Schrödinger equations.

Huian Lin1, Liming Ling1

  • 1School of Mathematics, South China University of Technology, Guangzhou 510641, China.

Chaos (Woodbury, N.Y.)
|April 5, 2024
PubMed
Summary
This summary is machine-generated.

This study explores multi-component derivative nonlinear Schrödinger equations, deriving higher-order vector rogue wave solutions. The research analyzes asymptotic behaviors and patterns, particularly with large parameters, revealing connections to polynomial hierarchies.

More Related Videos

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
15:06

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

12.9K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.6K

Related Experiment Videos

Last Updated: Jun 29, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.0K
Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
15:06

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

Published on: January 3, 2016

12.9K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.6K

Area of Science:

  • Nonlinear Physics
  • Mathematical Physics
  • Optical Solitons

Background:

  • Nonlinear Schrödinger equations are fundamental in describing wave phenomena.
  • Derivative nonlinear Schrödinger (n-DNLS) equations extend these models with complex dynamics.
  • Nonzero boundary conditions are crucial for realistic physical scenarios.

Purpose of the Study:

  • To derive higher-order vector rogue wave solutions for multi-component n-DNLS equations.
  • To analyze the asymptotic dynamics and pattern classification of these solutions.
  • To investigate solutions under specific conditions, including large parameter limits.

Main Methods:

  • Darboux transformation method for constructing solutions.
  • Analysis of characteristic polynomials with multiple roots.
  • Asymptotic analysis of dynamic behaviors.

Main Results:

  • Explicit higher-order vector rogue wave solutions derived.
  • Identification of specific solution patterns linked to root structures.
  • Detailed analysis of asymptotic dynamics for large parameter regimes.

Conclusions:

  • The Darboux transformation effectively yields complex rogue wave solutions.
  • Asymptotic analysis reveals rich pattern classifications in n-DNLS systems.
  • Findings contribute to understanding nonlinear wave phenomena in multi-component systems.