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

Search research articles

Related Experiment Videos

Multiphase control of a nonlinear lattice.

M Khasin¹, L Friedland

¹Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.

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

|February 3, 2004

Summary

Researchers demonstrate precise control over large amplitude excitations in the Toda lattice using small external forces. This method achieves stable, multiphase self-locking through adiabatic resonance passage, enabling tunable n-gap solutions.

Related Concept Videos

You might also read

Related Articles

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

Sort by

Same author

Multiphase autoresonant excitations in the Korteweg-de Vries system.

Physical review. E·2025

Same author

Autoresonant generation of solitons in Bose-Einstein condensates by modulation of the interaction strength.

Physical review. E·2024

Same author

Parametric autoresonant generation of dark solitons.

Physical review. E·2022

Same author

Narrow autoresonant magnetization structures in finite-length ferromagnetic nanoparticles.

Physical review. E·2019

Same author

Autoresonant excitation of Bose-Einstein condensates.

Physical review. E·2018

Same author

Parametric autoresonant excitation of the nonlinear Schrödinger equation.

Physical review. E·2016

Area of Science:

Nonlinear Dynamics
Lattice Systems
Mathematical Physics

Background:

The periodic Toda lattice is a fundamental model in nonlinear dynamics.
Generating and controlling large amplitude, multiphase excitations (n-gap solutions) presents significant challenges.

Purpose of the Study:

To develop a method for creating and controlling large amplitude, multiphase excitations in the periodic Toda lattice.
To investigate the mechanism of phase synchronization and self-locking under adiabatic perturbations.

Main Methods:

Utilizing passage through an ensemble of resonances to initiate excitation.
Employing adiabatic wave-like perturbations for multiphase self-locking.
Analyzing the system's behavior from weakly nonlinear to fully nonlinear stages.

Main Results:

Demonstrated creation and control of n-gap solutions via small forcing.
Identified a robust phase-locking mechanism in the weakly nonlinear stage, dependent on forcing amplitude and frequency chirp rate.
Showcased adiabatic synchronization into a stable, persistent multifrequency resonance in the fully nonlinear stage.

Conclusions:

Complete control over n-gap states in the Toda lattice is achievable.
Slow variation of external parameters allows for precise tuning of the system's multifrequency resonant state.

Related Experiment Videos