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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...
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A quadratic equation in the form ax2+bx+c=0 can have solutions that vary in nature depending on the value of the discriminant, b2−4ac. In this expression, a is the coefficient of the quadratic term x2, b is the coefficient of the linear term x, and c is the constant term. When the discriminant is negative, the equation has no real number solutions. However, by introducing complex numbers through the imaginary unit i, defined by i=-1, these equations can still be solved.The square root of a...
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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...

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Updated: Jun 3, 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

Parametrically driven pure-quartic solitons.

Pengfei Li, Lijing Xing, Dongdong Wang

    Optics Letters
    |June 1, 2026
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces quiescent and moving parametrically driven pure-quartic solitons (PDPQSs), expanding the understanding of self-trapped modes. Elastic collisions between stable PDPQSs were observed, highlighting their robust dynamics.

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    Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
    09:23

    Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

    Published on: May 30, 2014

    Area of Science:

    • Nonlinear physics
    • Optical solitons
    • Mathematical modeling

    Background:

    • Parametrically driven solitons are established self-trapped modes in diverse physical systems.
    • Previous research focused on solitons with second-order group-velocity dispersion (GVD), linear loss, parametric gain, and cubic nonlinearity.

    Purpose of the Study:

    • To report the existence of quiescent parametrically driven pure-quartic solitons (PDPQSs) in a comprehensive system.
    • To investigate moving PDPQSs in the absence of losses.
    • To analyze the stability domains and dynamics of these novel solitons.

    Main Methods:

    • Systematic analysis of soliton existence and stability within the parameter space.
    • Exploration of the evolution of unstable soliton states.
    • Numerical simulations to observe soliton collisions.

    Main Results:

    • Existence of quiescent PDPQSs in the full system (including quartic potential).
    • Existence of moving PDPQSs in the absence of losses.
    • Identification of specific stability domains for PDPQSs.
    • Demonstration of elastic collisions between traveling stable PDPQSs.

    Conclusions:

    • Parametrically driven pure-quartic solitons represent a new class of solitons with unique properties.
    • The identified stability domains are crucial for potential applications.
    • Elastic collisions suggest potential for stable propagation and interaction in nonlinear systems.