Cross-Overs of Bramson’s Shift at the Transition Between Pulled and Pushed Fronts

The Bramson logarithmic shift of the position of pulled fronts is a universal feature common to a large class of monostable traveling wave equations. As one varies the non-linearities it so happens that one can observe, at some critical non linearity, a transition from pulled fronts to pushed fronts...

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Bibliographic Details
Published inJournal of statistical physics Vol. 190; no. 3
Main Author Derrida, Bernard
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2023
Springer
Springer Nature B.V
Subjects
Crossovers
Initial conditions
Mathematical and Computational Physics
Mathematical models
Nonlinearity
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Traveling waves
Wave equations
Travelling waves
Fisher–KPP equation
Bramson shift
Cut-offs
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Summary:The Bramson logarithmic shift of the position of pulled fronts is a universal feature common to a large class of monostable traveling wave equations. As one varies the non-linearities it so happens that one can observe, at some critical non linearity, a transition from pulled fronts to pushed fronts. At this transition the Bramson shift is modified. In the limit where time goes to infinity and the non-linearity becomes critical, the position of the front exhibits a cross-over. The goal of the present note is to give the expression of this cross-over function, for a particular model which is exactly soluble, with the hope that this expression would remain valid for more general traveling wave equations at the transition between pulled and pushed fronts. Other cross-over functions are also obtained, for this particular model, to describe the dependence on initial conditions or the effect of a cut-off.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-023-03077-8