Annihilation of two interfaces in a hybrid system

Abstract

We consider the mixed ODE-PDE system called a hybrid system, in which the two interfaces interact with each other through a continuous medium and their equations of motion are derived in a weak interaction frame- work. We study the bifurcation property of the resulting hybrid system and construct an unstable standing pulse solution, which plays the role of a sepa- rator for dynamic transition from standing breather to annihilation behavior between two interfaces.