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Related Concept Videos

Propagation of Waves01:07

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...
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

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. 
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The de Broglie Wavelength02:32

The de Broglie Wavelength

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Travelling Waves01:04

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A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
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Equations of Wave Motion01:02

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Related Experiment Video

Updated: May 26, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

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Published on: December 4, 2017

Nonlinear wave propagation in a gravitating quantum fluid.

Samiran Ghosh1, Nikhil Chakrabarti

  • 1Department of Applied Mathematics, University of Calcutta 92, Acharya Prafulla Chandra Road, Kolkata 700 009, India. sran−g@yahoo.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
PubMed
Summary

Nonlinear waves in Bose-Einstein condensates are described by a novel Korteweg-de Vries equation. Quantum and gravitational effects create unique soliton-like solutions.

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Last Updated: May 26, 2026

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Area of Science:

  • Quantum physics
  • Fluid dynamics
  • Gravitational physics

Background:

  • Bose-Einstein condensates exhibit complex behaviors under external influences.
  • Understanding nonlinear wave propagation is crucial for describing quantum fluid dynamics.

Purpose of the Study:

  • To investigate nonlinear wave propagation in a Bose-Einstein condensate gas under gravitational influence.
  • To derive and analyze a governing equation for small-amplitude dynamics.

Main Methods:

  • Utilized a gravitating quantum fluid model.
  • Derived a Korteweg-de Vries equation with a nonlocal term.
  • Solved the derived equation analytically.

Main Results:

  • The small-amplitude dynamics are governed by a Korteweg-de Vries equation with a nonlocal term.
  • Quantum effects provide dispersion, while gravity introduces the nonlocal term.
  • A novel, analytically solved soliton-like solution was obtained.

Conclusions:

  • The study presents a new model for nonlinear waves in gravitating Bose-Einstein condensates.
  • The findings highlight the interplay between quantum dispersion and gravitational nonlocality.
  • The soliton-like solution has potential implications for understanding collective phenomena in such systems.