Multidimensional Stability of Waves Travelling Through Rectangular   Lattices in Rational Directions
  We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small perturbations. We employ recently developed techniques involving point-wise Green's functions estimates for functional differential equations of mixed type (MFDEs), allowing our results to be applied even in situations where comparison principles are not available. 
A. Hoffman, H. J. Hupkes, E. Van Vleck
math.AP math.DS