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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
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Soliton: A dispersion-less solution with existence and its types.
Geeta Arora1, Richa Rani1, Homan Emadifar2
1Department of Mathematics, Lovely Professional University, Phagwara, Punjab, India.
Heliyon
|December 26, 2022
Summary
Solitons are solitary waves that maintain energy and speed. This article explores their discovery, types, and diverse applications in fields like nonlinear optics and biophysics.
Area of Science:
- Nonlinear Dynamics and Mathematical Physics
Background:
- Solitons are unique, stable wave solutions to nonlinear partial differential equations.
- They exhibit particle-like properties, traveling without energy dissipation or shape change.
Purpose of the Study:
- To provide a historical overview of soliton discovery.
- To classify different types of solitons.
- To explore the diverse applications of solitons across scientific disciplines.
Main Methods:
- Analysis of solution behavior for key nonlinear equations: Korteweg-de Vries (KdV), sine-Gordon (SG), Camassa-Holm (CH), and nonlinear Schrödinger (NLS).
Main Results:
- Discussion of the fundamental properties and behavior of solitons derived from these equations.
- Categorization of solitons based on their characteristics.
Conclusions:
- Solitons represent a significant phenomenon in nonlinear science.
- Their predictable behavior and stability lead to widespread applications in various scientific and technological fields.
Keywords:
Camassa-Holm equationKorteweg de Vries equationNonlinear Schrodinger equationProperties of solitonsSolitonssine-Gordon equationMore Related Videos
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