We use the Maslov index to study the spectrum of a class of linear Hamiltonian differential
operators. We provide a lower bound on the number of positive real eigenvalues, which …

We consider inhomogeneous non-linear wave equations of the type utt= uxx+ V′(u, x)− αut
(α⩾ 0). The spatial real axis is divided in intervals Ii, i= 0,…, N+ 1 and on each individual …

In this manuscript, we consider the impact of a small jump-type spatial heterogeneity on the
existence of stationary localized patterns in a system of partial differential equations in one …

In this article, a general geometric singular perturbation framework is developed to study the
impact of strong, spatially localized, nonlinear impurities on the existence, stability and …

We extend the definition of the Maslov index to a broad class of non-Hamiltonian dynamical
systems. To do this, we introduce a family of topological spaces---which we call Maslov …

This paper presents an introduction to the existence and stability of stationary fronts in wave
equations with finite length spatial inhomogeneities. The main focus will be on wave …

A central theme underpinning this thesis is “a beautiful connection between analysis,
dynamics and topology"[Bec20], which can be found in the 19th century Sturmian theory of …

We introduce the conception of flat-bottom dark gap modes in one-dimensional periodic
nanostructures configured as periodic alternations (nanoscale stripes) of the local linear and …

Exchange of energy by means of light-matter interaction provides a new dimension to
various nonlinear dynamical systems. Here, the effects of light-matter interaction are …

We extend the definition of the Maslov index to a broad class of non-Hamiltonian dynamical
systems. To do this, we introduce a family of topological spaces—which we call Maslov …