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Related Concept Videos

Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Shock Waves01:16

Shock Waves

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 pressures...
Interference and Superposition of Waves01:07

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,...
Solvating Effects02:12

Solvating Effects

An understanding of the solvating effect helps rationalize the relation between solvation and acidity of the compound. In addition, this also explains the relative stability of conjugate bases for compounds with different pKa values. This lesson details, in-depth, the principle of solvating effects. The strength of an acid and the stability of its corresponding conjugate base are determined using pKa values. This observed relationship is a consequence of solvation, which is the interaction...
Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...

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Related Experiment Video

Updated: Jun 12, 2026

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

Soliton explosion control by higher-order effects.

Sofia C V Latas1, Mário F S Ferreira

  • 1Department of Physics, University of Aveiro, 3810-193 Aveiro, Portugal.

Optics Letters
|June 3, 2010
PubMed
Summary
This summary is machine-generated.

Higher-order effects in optical solitons can be managed. Conjugating effects like self-frequency shift and self-steepening eliminates pulse explosions, enabling stable pulse propagation.

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Area of Science:

  • Nonlinear optics
  • Soliton dynamics
  • Complex Ginzburg-Landau equation

Background:

  • Solitons are robust optical pulses, but higher-order effects can cause instability.
  • The quintic complex Ginzburg-Landau equation models these complex pulse dynamics.
  • Understanding and controlling pulse explosions is crucial for applications.

Purpose of the Study:

  • To numerically investigate the influence of higher-order effects on soliton solutions.
  • To identify conditions for eliminating pulse explosions.
  • To explore the potential for stable soliton propagation.

Main Methods:

  • Numerical simulations of the quintic complex Ginzburg-Landau equation.
  • Analysis of pulse evolution under varying higher-order dispersion, self-frequency shift, and self-steepening parameters.
  • Investigating pairwise and simultaneous conjugation of these effects.

Main Results:

  • Pulse explosions in soliton solutions can be eliminated through specific conjugations of higher-order effects.
  • Positive third-order dispersion compensates for self-frequency shift.
  • Negative third-order dispersion compensates for self-steepening.

Conclusions:

  • The interplay of self-frequency shift, self-steepening, and third-order dispersion significantly impacts soliton stability.
  • Careful management of these higher-order effects allows for the complete suppression of pulse explosions.
  • Stable, fixed-shape pulse propagation is achievable even with the simultaneous presence of these three effects.