We determine and study the ground states of a focusing Schrödinger equation in dimension
one with a power nonlinearity| ψ| 2 μ ψ and a strong inhomogeneity represented by a …

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 …

The nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting
over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) …

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 …

The Swift–Hohenberg equation describes an instability which forms finite-wavenumber
patterns near onset. We study this equation posed with a spatial inhomogeneity; a jump-type …

We consider a Josephson junction system installed with a finite length inhomogeneity, either
of micro-resistor or micro-resonator type. The system can be modelled by a sine-Gordon …

A periodically inhomogeneous Schrödinger equation is considered. The inhomogeneity is
reflected through a non-uniform coefficient of the linear and nonlinear term in the equation …

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 …