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

Navier–Stokes Equations

Navier–Stokes Equations

For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...

Ampere-Maxwell's Law: Problem-Solving

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...

Propagation of Waves

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

Interference and Superposition of Waves

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...

Equations of Wave Motion

Equations of Wave Motion

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.

You might also read

Related Articles

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

Sort by

Same author

Solving the coupled Gerdjikov-Ivanov equation via Riemann-Hilbert approach on the half line.

Scientific reports·2025

Same author

Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves.

Chaos (Woodbury, N.Y.)·2023

Same author

On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions.

Heliyon·2023

Same author

The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method.

Computational intelligence and neuroscience·2021

Same author

The Short-Term Load Forecasting Using an Artificial Neural Network Approach with Periodic and Nonperiodic Factors: A Case Study of Tai'an, Shandong Province, China.

Computational intelligence and neuroscience·2021

Same author

The Short-Term Load Forecasting for Special Days Based on Bagged Regression Trees in Qingdao, China.

Computational intelligence and neuroscience·2021

Search research articles

Related Experiment Video

Updated: Jun 20, 2025

Author Spotlight: Advancing Large-Scale Neural Dynamics Through HD-MEA Technology

Author Spotlight: Advancing Large-Scale Neural Dynamics Through HD-MEA Technology

Published on: March 8, 2024

Data-driven rogue waves solutions for the focusing and variable coefficient nonlinear Schrödinger equations via deep

Jiuyun Sun¹, Huanhe Dong¹, Mingshuo Liu¹

¹College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.

Chaos (Woodbury, N.Y.)

|July 19, 2024

Summary

This study uses deep learning, specifically physics-informed memory networks (PIMNs), to accurately solve for rogue wave solutions in nonlinear Schrödinger equations. The method effectively captures complex nonlinear dynamics, advancing AI in solving differential equations.

More Related Videos

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Published on: August 12, 2018

Related Experiment Videos

Last Updated: Jun 20, 2025

Author Spotlight: Advancing Large-Scale Neural Dynamics Through HD-MEA Technology

Author Spotlight: Advancing Large-Scale Neural Dynamics Through HD-MEA Technology

Published on: March 8, 2024

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Targeting Neuronal Fiber Tracts for Deep Brain Stimulation Therapy Using Interactive, Patient-Specific Models

Published on: August 12, 2018

Area of Science:

Nonlinear Dynamics
Computational Physics
Artificial Intelligence

Background:

Rogue waves are extreme amplitude events in nonlinear systems.
Nonlinear Schrödinger (NLS) equations model various wave phenomena, including rogue waves.
Solving complex differential equations often requires advanced numerical methods.

Purpose of the Study:

To investigate data-driven rogue wave solutions for focusing and variable coefficient NLS equations.
To apply physics-informed memory networks (PIMNs) for solving these equations.
To analyze the impact of network parameters on solution accuracy.

Main Methods:

Utilizing physics-informed memory networks (PIMNs) for a data-driven approach.
Solving first- and second-order rogue wave solutions for the focusing NLS equation.
Solving three deformed rogue wave solutions for the variable coefficient NLS equation.
Examining the influence of optimization algorithms, network structure, and mesh size.

Main Results:

PIMNs successfully captured the nonlinear features of rogue wave solutions.
Demonstrated high accuracy in solving both standard and deformed rogue wave scenarios.
Numerical experiments confirmed the effectiveness of the deep learning approach.

Conclusions:

PIMNs are a powerful tool for accurately solving nonlinear Schrödinger equations.
This deep learning method offers significant potential for understanding rogue wave dynamics.
The study highlights the advancement of AI in tackling complex partial differential equations.