Related Experiment Video
Updated: Jun 8, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Transition from modulated to exploding dissipative solitons: hysteresis, dynamics, and analytic aspects.
Orazio Descalzi1, Helmut R Brand
1Universidad de los Andes, Av. San Carlos de Apoquindo 2200, Santiago, Chile. odescalzi@miuandes.cl
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
This study explores exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation. We found transitions to these solitons occur through a hysteretic process, with increasing symmetry as parameters change.
Area of Science:
- Nonlinear Optics
- Mathematical Physics
- Complex Systems
Background:
- Dissipative solitons are localized waves in systems with energy gain and loss.
- Akhmediev's group previously identified exploding dissipative solitons.
- The cubic-quintic complex Ginzburg-Landau equation models various nonlinear phenomena.
Purpose of the Study:
- To investigate the properties and transition mechanisms of exploding dissipative solitons.
- To analyze the influence of the parameter μ (distance from linear onset) on soliton behavior.
- To characterize the dynamics leading to the formation of exploding solitons.
Main Methods:
- Numerical simulations of the cubic-quintic complex Ginzburg-Landau equation.
- Systematic variation of the parameter μ while keeping other parameters fixed.
- Analytical study of the collapse time for exploding solitons.
Main Results:
- Observed a range of soliton behaviors including stationary, rapidly oscillating, and frequency-modulated pulses as μ increased.
- Identified a hysteretic transition to exploding solitons involving symmetric and asymmetric two-frequency pulses.
- Found that increasing μ in the exploding soliton regime favors symmetric solitons, with asymmetric solitons dominating at the transition point.
Conclusions:
- The transition to exploding dissipative solitons is a complex hysteretic process.
- Soliton symmetry is influenced by the parameter μ, showing a trend towards increased symmetry.
- Analytical results for collapse time show good agreement with numerical findings, validating the models used.
Related Concept Videos
01:20Types of Damping
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
01:19Limits with Oscillating Discontinuities
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
02:39Phase Transitions: Vaporization and Condensation
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
01:07Damped Oscillations
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
01:15Theories of Dissolution: Diffusion Layer Model
Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
01:18Second 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...
If ζ...