Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Collisions in Multiple Dimensions: Problem Solving

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...

Collisions in Multiple Dimensions: Introduction

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...

$Interference and Diffraction$ 02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

Elastic Collisions: Case Study

Elastic Collisions: Case Study

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...

Elastic Collisions: Introduction

Elastic Collisions: Introduction

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...

Gravity between Spherical Bodies

Gravity between Spherical Bodies

Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Radiation in bent asymmetric coupled waveguides.

Applied optics·2019

Same author

Intramural colonic haematoma with fistula formation in a haemophiliac.

Irish journal of medical science·2016

Same author

Intramural duodenal haematoma in a haemophiliac.

Irish journal of medical science·2016

Same author

On the asymptotic evolution of finite energy Airy wave functions.

Optics letters·2015

Same author

Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics.

Physical review letters·2012

Same author

Ultrabroad-bandwidth multifrequency Raman soliton pulse trains.

Optics letters·2009

Search research articles

Related Experiment Video

Updated: Jul 19, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Spatial Kerr soliton collisions at arbitrary angles.

P Chamorro-Posada¹, G S McDonald

¹Departamento de Teoría de la Señal y Comunicaciones e Ingeniería Telemática, Universidad de Valladolid, ETSI Telecomunicación, Campus Miguel Delibes s/n, 47011 Valladolid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 10, 2006

Summary

We expanded the theory of spatial Kerr solitons to include non-copropagating and non-counterpropagating colliding beams. Our new method shows Kerr solitons are robust even under these complex, nonparaxial collision conditions.

More Related Videos

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators

Published on: April 4, 2016

Rejection of Fluorescence Background in Resonance and Spontaneous Raman Microspectroscopy

Rejection of Fluorescence Background in Resonance and Spontaneous Raman Microspectroscopy

Published on: May 18, 2011

Related Experiment Videos

Last Updated: Jul 19, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators

Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators

Published on: April 4, 2016

Rejection of Fluorescence Background in Resonance and Spontaneous Raman Microspectroscopy

Rejection of Fluorescence Background in Resonance and Spontaneous Raman Microspectroscopy

Published on: May 18, 2011

Area of Science:

Nonlinear Optics
Mathematical Physics

Background:

Spatial Kerr solitons are fundamental in nonlinear optics.
Existing theories often rely on paraxial approximations, limiting their applicability to specific beam collision geometries.

Purpose of the Study:

To extend the theory of spatial Kerr solitons to nonparaxial colliding beams.
To develop a formalism that accounts for the inherent symmetry of collision processes.
To investigate the robustness of Kerr solitons under nonparaxial collisions.

Main Methods:

Development of a new Helmholtz formalism for soliton collisions.
Numerical simulations of soliton collisions.
Approximate analytical calculations.

Main Results:

The new formalism provides results consistent with collision symmetry.
The theory predicts phenomena not covered by paraxial descriptions.
Excellent agreement was found between numerical and analytical results.
Spatial Kerr solitons demonstrate remarkable robustness under nonparaxial collisions.

Conclusions:

The developed Helmholtz formalism accurately describes nonparaxial Kerr soliton collisions.
Kerr solitons exhibit high stability even in complex collision scenarios.
This work expands the understanding of soliton dynamics in nonlinear media.