Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 101 - 124, Volume 32, Issue 1, January 2012      doi:10.3934/dcds.2012.32.101

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Jong-Shenq Guo - Department of Mathematics, Tamkang University, 151, Ying-Chuan Road, Tamsui, Taipei County 25137, Taiwan (email)
Ying-Chih Lin - Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677, Taiwan (email)

Abstract: 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.

Keywords:  Lattice dynamical system, traveling wave, monotonicity, uniqueness.
Mathematics Subject Classification:  Primary: 34K05, 34A34; Secondary: 34K60, 34E05.

Received: August 2010;      Revised: December 2010;      Available Online: September 2011.