Lattice travelling wave problems: Advanced-Retarded FDE BVPs, and a surprising sighting of symplectic Euler
Tony Humphries (McGill University, Canada)
Abstract. Many lattice differential equations appear to admit standing or travelling wave solutions. In applications (e.g., crystal growth, nerve conduction) it is important to know which occurs. However, this is a difficult question to answer, because travelling waves are defined by Advanced-Retarded Functional Differential Equations with the propagation failure limit as the wave speed vanishes being singular, whereas standing waves are defined by difference equations. This talk will focus on ongoing computational and analytical research near and at this singular limit. Problems and results will be illustrated using a spatially discrete Nagumo equation.