Structural Stability and Renormalization Group for Propagating Fronts
G.C. Paquette, Lin-Yuan Chen, Nigel Goldenfeld, Y. Oono (Physics, Department, University of Illinois at Urbana-Champaign)
TL;DR
This paper explores how structural stability can serve as a velocity selection principle for propagating fronts, using numerical and renormalization group methods to demonstrate this concept.
Contribution
It introduces the novel idea of using structural stability as a criterion for selecting front velocities in propagating solutions.
Findings
Structural stability can determine front velocity.
Numerical methods support the stability-based velocity selection.
Renormalization group methods are effective in analyzing propagating fronts.
Abstract
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using numerical and renormalization group methods.
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