2012/10/28 by Erik S. Van Vleck, Aijun Zhang, Van Vleck, Erik S. +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.1210.7502
openalex publication_date 2012/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The existence of traveling front solutions to bistable lattice differential equations in the absence of a comparison principle is studied. The results are in the spirit of those in Bates, Chen, and Chmaj in[1], but are applicable to vector equations and to more general limiting systems. An abstract result on the persistence of traveling wave solutions is obtained and is then applied to lattice differential equations with repelling first and/or second neighbor interactions and to some problems with infinite range interactions.