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Related Concept Videos

Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
Quadratic Equations01:29

Quadratic Equations

A quadratic equation is an algebraic expression where a variable is raised to the second power and combined with its first power and a constant; all equated to zero. These equations are frequently used to model relationships involving area, motion, and optimization. The general representation of a quadratic equation iswhere a, b, and c are real values, and a is nonzero to ensure the presence of the squared term.One method for solving a quadratic equation involves rewriting it as a product of...
Partial Differential Equations01:21

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
Kinematic Equations: Problem Solving01:15

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
Quadric Surfaces01:28

Quadric Surfaces

Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
Bessel Function of Order Zero01:20

Bessel Function of Order Zero

A common physical example of wave propagation with radial symmetry is the ripple formed when a stone is dropped into a still pond. The disturbance originates at a central point and travels outward as a circular wave. As the radius of the wavefront increases, the same initial energy is distributed along a progressively larger circumference. Consequently, the amplitude, or height, of the wave decreases with distance from the center. This decay behavior cannot be captured by simple sine or cosine...

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Related Experiment Video

Updated: Jun 23, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
07:42

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Simple physics of quadratic spatial solitons.

Gaetano Assanto, George Stegeman

    Optics Express
    |May 14, 2009
    PubMed
    Summary

    Spatial solitons in nonlinear media are explained through parametric gain, diffraction, and cascading. This study offers an intuitive physical interpretation of their formation, propagation, and interactions.

    Area of Science:

    • Nonlinear Optics
    • Quantum Optics
    • Mathematical Physics

    Background:

    • Spatial solitons are self-trapping beams in nonlinear optical media.
    • Their behavior is governed by a balance between diffraction and nonlinear effects.
    • Previous studies focused on mathematical descriptions and experimental observation.

    Purpose of the Study:

    • To provide an intuitive physical interpretation of spatial solitons in quadratically nonlinear media.
    • To elucidate the processes governing soliton excitation, propagation, and collisions.
    • To bridge the gap between mathematical models and physical understanding.

    Main Methods:

    • Analysis of the interplay between parametric gain, diffraction, and cascading phase shift.
    • Development of an intuitive physical model for soliton dynamics.

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    Published on: December 4, 2017

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    Last Updated: Jun 23, 2026

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
    07:42

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

    Published on: December 15, 2021

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

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

    Published on: December 4, 2017

  • Qualitative description of excitation, propagation, and collisional interactions.

    • Main Results:

    • An accessible explanation of the underlying physics of spatial solitons.
    • Clear outline of the mechanisms driving soliton behavior.
    • Understanding of how solitons are excited, propagate, and interact.

    Conclusions:

    • The physics of spatial solitons in quadratically nonlinear media can be intuitively understood.
    • This interpretation aids in comprehending their complex behaviors.
    • Facilitates further research and applications of spatial solitons.