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Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law.
V N Biktashev1,2, M A Tsyganov3
1College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK.
Scientific Reports
|August 6, 2016
Summary
This study shows that quasi-solitons, robust nonlinear waves, can exist in excitable systems with only self-diffusion. This finding simplifies the study of complex wave behaviors in multi-component systems.
Area of Science:
- Nonlinear dynamics
- Mathematical physics
- Chemical kinetics
Background:
- Solitons are nonlinear waves found in conservative systems.
- Quasi-solitons appear in dissipative systems near bifurcations or with cross-diffusion.
- Excitable systems exhibit complex dynamics.
Purpose of the Study:
- To demonstrate robust quasi-soliton observation in excitable systems with only self-diffusion.
- To explain the emergence of quasi-solitons through effective cross-diffusion.
- To introduce a reduction procedure for analyzing complex wave regimes.
Main Methods:
- Analysis of excitable systems with excitable kinetics and self-diffusion.
- Adiabatic elimination of fast diffusing components to derive effective cross-diffusion.
- Development of a reduction procedure for multi-component systems.
Main Results:
- Quasi-solitons of fixed shape and envelope quasi-solitons are robustly observed.
- Effective cross-diffusion emerges from adiabatic elimination.
- The reduction procedure simplifies the study of complex wave phenomena.
Conclusions:
- Quasi-solitons are not limited to systems with cross-diffusion or finely tuned parameters.
- Adiabatic elimination provides a mechanism for quasi-soliton formation in simpler systems.
- The reduction procedure facilitates the investigation of complex wave behaviors in stiff, multi-component systems.
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