Effect on Pulled Fronts

The starting point of Brunet and Derrida s approach is to replace the kinetic term in the FKPP equation by F p) = 0 p — e)p - p). Here 9 -) denotes the Heaviside function, and e = 1/A is the cutoff, where N is the average number of particles in the state p = 1. In the frame comoving with the front, the RD equation 

At the boundary between regions I and II and the boundary between II and III, the particle density p, as well as its comoving derivative p, must be continuous. Since e -C 1, the solutions of (4.81) are given to leading order by 

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