Mathematische Annalen

, Volume 326, Issue 1, pp 123–146 | Cite as

Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics

  • Xinfu Chen
  • Jong-Shenq Guo


 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 cmin such that a traveling wave of speed c exists if and only if ccmin. 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.


Discrete System Monostable Dynamic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Xinfu Chen
    • 1
  • Jong-Shenq Guo
    • 2
  1. 1.Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA (e-mail:
  2. 2.Department of Mathematics, National Taiwan Normal University, Taipei 117, Taiwan (e-mail:

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