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

Differential Equations: Problem Solving

Differential Equations: Problem Solving

When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...

Transmission-Line Differential Equations

Transmission-Line Differential Equations

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 the...

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...

Linear Differential Equations

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...

Separable Differential Equations

Separable Differential Equations

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...

Poisson's And Laplace's Equation

Poisson's And Laplace's Equation

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.

You might also read

Related Articles

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

Sort by

Same author

[Effect of Three Typical Disinfection Byproducts on Bacterial Antibiotic Resistance].

Huan jing ke xue= Huanjing kexue·2015

Same author

microRNA deregulation in keloids: an opportunity for clinical intervention?

Cell proliferation·2015

Same author

The role of TARBP2 in the development and progression of cancers.

Tumour biology : the journal of the International Society for Oncodevelopmental Biology and Medicine·2015

Same author

The role of miRNAs in the pheochromocytomas.

Tumour biology : the journal of the International Society for Oncodevelopmental Biology and Medicine·2015

Same author

Abnormalities of cingulate cortex in antipsychotic-naïve chronic schizophrenia.

Brain research·2015

Same author

Pulse Pressure Variation Adjusted by Respiratory Changes in Pleural Pressure, Rather Than by Tidal Volume, Reliably Predicts Fluid Responsiveness in Patients With Acute Respiratory Distress Syndrome.

Critical care medicine·2015

Search research articles

Related Experiment Video

Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Soliton management for a variable-coefficient modified Korteweg-de Vries equation.

Zhi-Yuan Sun¹, Yi-Tian Gao, Ying Liu

¹Ministry-of-Education Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China.

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

|September 21, 2011

Summary

This study explores soliton management in a variable-coefficient modified Korteweg-de Vries equation, finding that solitons and breathers can be controlled by adjusting coefficients.

Related Experiment Videos

Last Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Nonlinear dynamics
Mathematical physics

Background:

Soliton management is crucial in Bose-Einstein condensates and optical fibers.
Variable-coefficient modified Korteweg-de Vries equations model interfacial waves and Alfvén waves.

Purpose of the Study:

Investigate soliton management for variable-coefficient modified Korteweg-de Vries equations.
Determine if soliton management concepts extend to these equations.

Main Methods:

Painlevé test to construct a generalized integrable form.
Ablowitz-Kaup-Newell-Segur system to establish a Lax pair.
Hirota bilinear method to derive multisoliton solutions.

Main Results:

A generalized integrable form was constructed under Painlevé constraints.
A Lax pair with time-dependent nonisospectral flow was established under stricter Lax constraints.
Multisoliton solutions were derived, demonstrating control over soliton and breather properties.

Conclusions:

Soliton management is feasible for variable-coefficient modified Korteweg-de Vries equations.
Variable coefficients allow for tuning soliton amplitude and width.
This research extends soliton management to new physical systems.