# American Institute of Mathematical Sciences

January  2012, 32(1): 101-124. doi: 10.3934/dcds.2012.32.101

## Traveling wave solution for a lattice dynamical system with convolution type nonlinearity

 1 Department of Mathematics, Tamkang University, 151, Ying-Chuan Road, Tamsui, Taipei County 25137 2 Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan

Received  August 2010 Revised  December 2010 Published  September 2011

We study traveling wave solutions for a lattice dynamical system with convolution type nonlinearity. We consider the monostable case and discuss the asymptotic behaviors, monotonicity and uniqueness of traveling wave. First, we characterize the asymptotic behavior of wave profile at both wave tails. Next, we prove that any wave profile is strictly decreasing. Finally, we prove the uniqueness (up to translation) of wave profile for each given admissible wave speed.
Citation: Jong-Shenq Guo, Ying-Chih Lin. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete & Continuous Dynamical Systems - A, 2012, 32 (1) : 101-124. doi: 10.3934/dcds.2012.32.101
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