# American Institute of Mathematical Sciences

April  2016, 36(4): 2329-2346. doi: 10.3934/dcds.2016.36.2329

## Entire solutions with merging fronts to a bistable periodic lattice dynamical system

 1 Department of Mathematics, Xidian University, Xi’an, Shaanxi 710071 2 Department of Mathematics, National Central University, Chung-Li 32001

Received  September 2014 Revised  July 2015 Published  September 2015

We are interested in finding entire solutions of a bistable periodic lattice dynamical system. By constructing appropriate super- and subsolutions of the system, we establish two different types of merging-front entire solutions. The first type can be characterized by two monostable fronts merging and converging to a single bistable front; while the second type is a solution which behaves as a monostable front merging with a bistable front and one chases another from the same side of $x$-axis. For this discrete and spatially periodic system, we have to emphasize that there has no symmetry between the increasing and decreasing pulsating traveling fronts, which increases the difficulty of construction of the super- and subsolutions.
Citation: Shi-Liang Wu, Cheng-Hsiung Hsu. Entire solutions with merging fronts to a bistable periodic lattice dynamical system. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 2329-2346. doi: 10.3934/dcds.2016.36.2329
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