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Tunable front interaction and localization of periodically forced waves.
Catherine Crawford1, Hermann Riecke
1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA. crawford@elmhurst.edu
Summary
Resonant temporal forcing stabilizes localized wave pulses in bistable systems by tuning front interactions. This method offers a novel way to control wave pulse stability in nonlinear systems.
Area of Science:
- Nonlinear dynamics
- Wave phenomena
- Complex systems
Background:
- Systems with bistability can host localized wave pulses formed by interacting fronts.
- The stability of these wave pulses is governed by the interplay between the fronts.
Purpose of the Study:
- To investigate the stabilization of localized wave pulses in bistable systems.
- To explore the role of resonant temporal forcing on wave pulse stability.
Main Methods:
- Analysis of wave pulses using coupled Ginzburg-Landau equations.
- Mathematical modeling of traveling-wave amplitudes.
Main Results:
- Resonant temporal forcing provides a tunable mechanism for stabilizing wave pulses.
- Temporal forcing can induce localization through both repulsive and attractive front interactions.
Conclusions:
- Temporal forcing offers a versatile method for controlling wave pulse stability.
- Findings are relevant to physical systems like binary-mixture convection and electroconvection in liquid crystals.