Behaviors of a front-back pulse arising in a bistable medium with jump-type heterogeneity

Abstract

We consider the dynamics of an oscillatory pulse (standing breather, SB) of front-back type, in which the motion of two interfaces that interact through a continuous field is described by a mixed ODE-PDE system. We carry out a center manifold reduction around the Hopf singularity of a stationary pulse solution, which provides us insight into the underlying mechanism for a sliding motion of SB in a jump-type spatial heterogeneous medium.