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

Separable Differential Equations01:20

Separable Differential Equations

295
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
295
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.1K
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
1.1K
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

1.4K
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
1.4K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

434
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....
434
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.6K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.6K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

61.6K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
61.6K

You might also read

Related Articles

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

Sort by
Same author

Dark-bright solitons with positive mass in Manakov cases with repulsive interactions.

Physical review. E·2025
Same author

Elliptic-rogue waves and modulational instability in nonlinear soliton equations.

Physical review. E·2024
Same author

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

Chaos (Woodbury, N.Y.)·2024
Same author

Exact analytical soliton solutions of N-component coupled nonlinear Schrödinger equations with arbitrary nonlinear parameters.

Physical review. E·2023
Same author

Phase characters of optical dark solitons with third-order dispersion and delayed nonlinear response.

Physical review. E·2022
Same author

Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning.

Physical review. E·2022

Related Experiment Video

Updated: Apr 3, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.5K

Integrable pair-transition-coupled nonlinear Schrödinger equations.

Liming Ling1, Li-Chen Zhao2

  • 1School of Mathematics, South China University of Technology, 510640, Guangzhou, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
PubMed
Summary
This summary is machine-generated.

This study reveals new nonlinear excitation dynamics in coupled systems, including novel breather transitions and rogue wave patterns, by analyzing exact solutions of the nonlinear Schrödinger equation. These findings offer insights into Bose-Einstein condensates and other complex nonlinear systems.

More Related Videos

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

9.8K
Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons
07:39

Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons

Published on: July 21, 2018

7.4K

Related Experiment Videos

Last Updated: Apr 3, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.5K
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

9.8K
Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons
07:39

Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons

Published on: July 21, 2018

7.4K

Area of Science:

  • Nonlinear physics
  • Quantum optics
  • Condensed matter physics

Background:

  • Coupled nonlinear Schrödinger equations (NLSE) model complex phenomena.
  • Pair particle transitions introduce unique dynamics.
  • Understanding nonlinear excitations is crucial for various physical systems.

Purpose of the Study:

  • To investigate integrable coupled NLSE with inter-component particle transitions.
  • To predict and characterize novel nonlinear excitation dynamics.
  • To explore potential experimental observations in Bose-Einstein condensates.

Main Methods:

  • Derivation of exact solutions for the coupled NLSE model.
  • Analysis of attractive and repulsive interaction cases.
  • Linear superposition of scalar NLSE solutions for coupled system solutions.

Main Results:

  • Prediction of striking transition dynamics for breathers.
  • Identification of new excitation patterns for rogue waves.
  • Discovery of stable topological kink excitations and other structures.

Conclusions:

  • Nonlinear wave solutions can be expressed as linear superpositions.
  • Findings are relevant to cigar-shaped Bose-Einstein condensates with two hyperfine states.
  • Results enhance understanding of nonlinear excitations in coupled systems like multimode fibers and waveguides.