AI Article Synopsis
- The research examines how fronts behave near a specific type of bifurcation in a mathematical framework known as the bistable Ginzburg-Landau equation.
- It involves creating precise front solutions and analyzing their stability, revealing that some solutions can be stable yet still not emerge from small initial conditions.
- The study also notes that certain conditions lead to instability, resulting in chaotic front behavior, which is further explored through numerical simulations.
Article Abstract
The speed and stability of fronts near a weakly subcritical steady-state bifurcation are studied, focusing on the transition between pushed and pulled fronts in the bistable Ginzburg-Landau equation. Exact nonlinear front solutions are constructed and their stability properties investigated. In some cases, the exact solutions are stable but are not selected from arbitrary small amplitude initial conditions. In other cases, the exact solution is unstable to modulational instabilities which select a distinct front. Chaotic front dynamics may result and is studied using numerical techniques.
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| http://dx.doi.org/10.1103/PhysRevE.96.032208 | DOI Listing |
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