We analyse pinned front and pulse solutions in a singularly perturbed three-component
FitzHugh–Nagumo model with a small jump-type heterogeneity. We derive explicit …

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 consider the NLS equation with a linear double-well potential. Symmetry breaking, ie the
localisation of an order parameter in one of the potential wells that can occur when the …

We study dark solitons near potential and nonlinearity steps and combinations thereof,
forming rectangular barriers. This setting is relevant to the contexts of atomic Bose-Einstein …

A nonlinear Schrödinger equation with repulsive (defocusing) nonlinearity is considered. As
an example, a system with a spatially varying coefficient of the nonlinear term is studied. The …

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 …