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

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Published on: December 4, 2017

Localized states beyond the asymptotic parametrically driven amplitude equation.

M G Clerc¹, S Coulibaly, D Laroze

¹Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.

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

|July 23, 2008

Summary

Researchers theoretically studied localized states in ferromagnetic spin chains and pendula chains. By adding higher-order terms to the nonlinear Schrödinger equation, they successfully identified these previously unaccounted-for states.

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Area of Science:

Condensed matter physics
Nonlinear dynamics

Background:

Easy-plane ferromagnetic spin chains and parametrically driven damped pendula chains exhibit complex behaviors under external fields.
Existing models, like the nonlinear Schrödinger equation, fail to capture certain localized states in these systems.

Purpose of the Study:

To theoretically investigate a family of localized states in driven magnetic and mechanical systems.
To extend the conventional nonlinear Schrödinger equation to include these states.

Main Methods:

Theoretical analysis of localized states.
Modification of the nonlinear Schrödinger equation by incorporating higher-order terms.

Main Results:

Identified a family of localized states connecting uniform oscillatory states.
Demonstrated that these states are not described by the standard nonlinear Schrödinger equation.
Successfully obtained these localized structures by augmenting the model.

Conclusions:

The inclusion of higher-order terms is crucial for accurately describing localized states in these driven nonlinear systems.
This work expands the understanding of complex dynamics in ferromagnetic spin chains and pendula chains.