The Evans function for nonlocal equations

Abstract

In recent studies of the master mode-locking equation, a model for solid-state cavity laser that includes nonlocal terms, bifurcations from stationary to seemingly time-periodic solitary waves have been observed.To decide whether the mechanism is a Hopf bifurcation or a bifurcation from the essential spectrum, a general framework for the Evans function for equations with nonlocal terms is developed and applied to the master mode-locking model.