%0 Journal Article
%T Existence and uniqueness of traveling waves in a class of unidirectional lattice differential equations
%A Aaron Hoffman
%A Benjamin Kennedy
%J Mathematics
%D 2008
%I arXiv
%X We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with unidirectional coupling. This class of lattice equations includes some spatial discretizations for hyperbolic conservation laws with a source term as well as a subclass of monotone systems. We obtain a variational characterization of the critical wave speed above which monotone traveling wave solutions are guaranteed to exist. We also discuss non-monotone waves, and the coexistence of monotone and non-monotone waves.
%U http://arxiv.org/abs/0809.2059v3