Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics

 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. Received: 28 February 2002 / Published online: 28 March 2003 This work was partially supported by the National Science Council of the Republic of China under the grants NSC 89-2735-M-001D-002 and 89-2115-M-003-014. Chen thanks the support from the National Science Foundation Grant DMS-9971043.