Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics

Abstract.

 We study traveling waves of a discrete system

where f and g are Lipschitz continuous with g increasing and f monostable, i.e., f(0)=f(1)=0 and f>0 on (0,1). We show that there is a positive c _min such that a traveling wave of speed c exists if and only if c≥c _min. Also, we show that traveling waves are unique up to a translation if f′(0)>0>f′(1) and g′(0)>0. The tails of traveling waves are also investigated.