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Related Concept Videos

Travelling Waves01:04

Travelling Waves

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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.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is...
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Shock Waves01:16

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While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high...
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Propagation of Waves01:07

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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.
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Reflection of Waves01:07

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When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
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Interference and Superposition of Waves01:07

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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.
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Traveling Waves: Lossless Lines01:27

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The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Transverse Instability of Rogue Waves.

Mark J Ablowitz1, Justin T Cole2

  • 1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA.

Physical Review Letters
|September 17, 2021
PubMed
Summary

Rogue wave models using the 2+1 dimensional nonlinear Schrödinger equation are unstable. Including transverse dimensions is crucial for accurately studying rogue wave phenomena.

Area of Science:

  • Fluid dynamics
  • Nonlinear optics
  • Wave physics

Background:

  • Rogue waves are unpredictable, large amplitude waves studied in various physical systems.
  • The (1+1) nonlinear Schrödinger equation models rogue waves using Peregrine and Kuznetov-Ma solitons.
  • The (2+1) hyperbolic nonlinear Schrödinger equation is suitable for systems with two transverse dimensions, like deep water waves and electromagnetic systems.

Purpose of the Study:

  • To investigate the stability of rogue wave solutions in the (2+1) hyperbolic nonlinear Schrödinger equation.
  • To determine the influence of transverse dimensions on rogue wave stability.
  • To assess the stability of the Peregrine soliton in this context.

Main Methods:

  • Analysis of the (2+1) hyperbolic nonlinear Schrödinger equation.

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  • Investigation of transverse instabilities in rogue wave solutions.
  • Comparison of Peregrine soliton stability with background plane wave stability.

    • Main Results:

    • Rogue wave solutions in the (2+1) model exhibit strong transverse instability across a range of frequencies.
    • The stability of the Peregrine soliton is directly linked to the stability of the background plane wave.
    • Transverse dimensions significantly impact the stability of rogue wave phenomena.

    Conclusions:

    • The (2+1) hyperbolic nonlinear Schrödinger equation reveals inherent instabilities in rogue wave solutions.
    • Transverse dynamics are essential for accurate rogue wave modeling, especially in deep water and electromagnetic contexts.
    • Ignoring transverse dimensions can lead to inaccurate predictions of rogue wave behavior.