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Kink topology control by high-frequency external forces in nonlinear Klein-Gordon models.
R Alvarez-Nodarse1, N R Quintero2, F G Mertens3
1Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Universidad de Sevilla, 41012 Sevilla, Spain and Departamento de Análisis Matemático, Universidad de Sevilla, apdo. 1160, E-41080, Sevilla, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 7, 2014
Summary
This study explores kink dynamics in the damped double sine-Gordon equation using averaging methods. High-frequency forces control kink appearance and reveal anomalous negative mobility.
Area of Science:
- Nonlinear dynamics
- Theoretical physics
- Computational physics
Background:
- The damped double sine-Gordon equation models complex physical systems.
- Understanding kink dynamics is crucial for various applications.
- External and parametric forces significantly influence system behavior.
Purpose of the Study:
- To investigate kink dynamics in the damped double sine-Gordon equation under high-frequency periodic forces.
- To analyze the effects of parametric and nonparametric driving forces.
- To explore the emergence of novel phenomena like negative mobility.
Main Methods:
- Application of a theoretical averaging method to simplify the complex dynamics.
- Derivation of an effective potential and an effective additive force for analysis.
- Direct numerical simulations of the original damped double sine-Gordon equation.
Main Results:
- The study successfully controls the appearance of two connected π kinks and individual π kinks by adjusting the driving frequency.
- An anomalous negative mobility phenomenon was theoretically predicted.
- Numerical simulations confirmed the predicted negative mobility, validating the theoretical approach.
Conclusions:
- Averaging methods provide effective insights into high-frequency driven nonlinear systems.
- Frequency control is a key parameter for manipulating kink configurations.
- The discovery of anomalous negative mobility opens new avenues for research in driven dissipative systems.
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