Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system
Zhaoquan Xu Jiying Ma
Discrete & Continuous Dynamical Systems - A 2015, 35(10): 5107-5131 doi: 10.3934/dcds.2015.35.5107
A delayed lattice dynamical system with non-local diffusion and interaction is considered in this paper. The exact asymptotics of the wave profile at both wave tails is derived, and all the wave profiles are shown to be strictly increasing. Moreover, we prove that the wave profile with a given admissible speed is unique up to translation. These results generalize earlier monotonicity, asymptotics and uniqueness results in the literature.
keywords: non-local diffusion and interaction. asymptotics uniqueness delayed lattice dynamical system monotonicity Travelling waves

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