Related Experiment Video
Updated: May 18, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
Published on: December 15, 2021
Wide localized solitons in systems with time- and space-modulated nonlinearities
L E Arroyo Meza1, A de Souza Dutra, M B Hott
1Universidade Estadual Paulista, Departamento de Física e Química, Guaratinguetá, São Paulo, Brazil. luisarroyo@feg.unesp.br
Abstract:
In this work we apply point canonical transformations to solve some classes of nonautonomous, nonlinear Schrödinger equations, namely, those which possess specific cubic and quintic (time- and space-dependent) nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wave function and recover a time- and space-independent nonlinear equation which can be solved explicitly. The method applied here allows us to find wide localized (in space) soliton solutions to the nonautonomous, nonlinear Schrödinger equation. We also generalize the external potential which traps the system and the terms of the nonlinearities.
More Related Videos
14:18Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
Published on: February 28, 2016
08:48Low-cost Custom Fabrication and Mode-locked Operation of an All-normal-dispersion Femtosecond Fiber Laser for Multiphoton Microscopy
Published on: November 22, 2019
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
State Space Representation
Consider an RLC circuit, a...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Region of Convergence of Laplace Tarnsform
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
Classification of Systems-I
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as: