Abstract
In this paper we consider a bistable lattice differential equation with competing first and second nearest neighbor interactions. We construct heteroclinic orbits connecting the stable zero equilibrium state with stable spatially periodic orbits of period p=2,3,4 using transform techniques and a bilinear bistable nonlinearity. We investigate the existence, global structure, and multiplicity of such traveling wave solutions. We show that in a certain parameter range the p=2 patterns have a finite maximum propagation speed. Our analysis also shows that multiple solutions involving a p=4 pattern may coexist at some velocities. Numerical simulations suggest the stability of some of the obtained solutions.
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