Related papers: Eigenvalue estimates for the scattering problem as…
We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of…
Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is…
We consider the eigenvalue problem for one-dimensional linear Schr\"odinger lattices (tight-binding) with an embedded few-sites linear or nonlinear, Hamiltonian or non-conservative defect (an oligomer). Such a problem arises when…
We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of…
We show that, after a transformation, the dynamics of linear perturbations (spin waves) around a singular Bloch point soliton is formally equivalent to a quantum system of an electron in a magnetic monopole field. The analytical solution to…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
This paper presents a comprehensive analysis of several aspects of the sinh-Gordon equation within a periodic setting. Our investigation proceeds in three main stages. First we establish the existence of periodic solutions for a fixed wave…
In this paper, we consider the problem of the scattering of in-plane waves at an interface between a homogeneous medium and a metamaterial. The relevant eigenmodes in the two regions are calculated by solving a recently described non…
The Hamiltonian-Krein (instability) index is concerned with determining the number of eigenvalues with positive real part for the Hamiltonian eigenvalue problem $ J L u=\lambda u$, where $J$ is skew-symmetric and $L$ is self-adjoint. If $J$…
In this paper, we study the almost sure scattering for the Klein-Gordon equations with Sobolev critical power. We obtain the almost sure scattering with random initial data in $H^s \times H^{s-1}$; $11/12 < s < 1$ for $d = 4$, $15/16 < s <…
The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the…
On a Riemannian manifold with or without boundary, and whether bounded or unbounded, we consider a semilinear wave (or Klein-Gordon) equation with a subcritical nonlinearity (either defocusing or focusing). We establish local…
We consider a one-body spin-less electron spectral problem for a resonance scattering system constructed of a quantum well weakly connected to a noncompact exterior reservoir, where the electron is free. The simplest kind of the resonance…
We review some recent results concerning integrable quantum field theories in 1+1 space-time dimensions which contain unstable particles in their spectrum. Recalling first the main features of analytic scattering theories associated to…
We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…
We explain the concept of Krein signature in Hamiltonian and $\mathcal{PT}$-symmetric systems on the case study of the one-dimensional Gross-Pitaevskii equation with a real harmonic potential and an imaginary linear potential. These…
The Steklov problem is an eigenvalue problem with the spectral parameter in the boundary conditions, which has various applications. Its spectrum coincides with that of the Dirichlet-to-Neumann operator. Over the past years, there has been…
We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…
In this survey paper we review classical results and recent progress about a certain topic in the spectral theory of two-dimensional canonical systems. Namely, we consider the questions whether the spectrum $\sigma$ is discrete, and if it…