We revisit the existence and stability of critical front in extended Fisher-KPP equation, refining earlier results Rottschäfer Wayne (J Differ Equ 176(2):532–560, 2001) which establish fronts without identifying a precise decay rate. Our main result states that is marginally spectrally stable, with essential spectrum touching imaginary axis but no unstable point spectrum. Together recent work A...

We consider a reaction-diffusion equation with a nonlinear term of the Fisher-KPP type, depending on time t and admitting two limits as t → ±∞. We derive the set of admissible asymptotic past and future speeds of transition fronts for such equation. We further show that any transition front which is non-critical as t → −∞ always admits two asymptotic past and future speeds. We finally describe ...

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonlinear reaction-diffusion equations into the soluti...

The Fisher equation, which combines di/usive motion of individuals with nonlinearities arising from their growth and competition processes, is analyzed, generalized, and applied to the dynamics of bacteria, pattern formation, and the spread of epidemics. Analytic solutions are also presented for some exactly soluble and physically relevant variants of the equation. c © 2004 Elsevier B.V. All ri...