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The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.…
We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a codimension-one stable manifold of the unique static…
Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special…
There has been a recent tendency to apply Schroedinger's wave equation to macroscopic domains, from Bose-Einstein condensates in neutron stars to planetary orbits. In these applications a hydrodynamical interpretation, involving vortices in…
We derive an exact solution for Stokes flow in an in a channel with permeable walls. We assume that at the channel walls, the normal component of the fluid velocity is described by Darcy's law and the tangential component of the fluid…
Chromonic liquid crystals are lyotropic nematic phases whose applications span from food to drug industries. It has recently been suggested that the elastic energy density governing the equilibrium distortions of these materials may be…
The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general…
The study of capillary wave scattering by a circular region with different interfacial properties from the rest of an otherwise homogeneous interface is motivated by experiments on wave attenuation at a monolayer covered air-water interface…
The two-dimensional sloshing problem is considered; it describes the transversal free oscillations of water in an open, infinitely long canal of uniform cross-section. It is proved that the fundamental eigenfrequency is simple, whereas the…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous…
The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study in particular the eigenfrequencies of an elastic disc with free boundaries and their connection to…
In this paper we combine a flexible covariant formulation of the shallow water equations with the semi-implicit numerical scheme developed over the years by Casulli and collaborators. After adopting an orthogonal, but non-orthonormal,…
A material that exhibits Willis coupling has constitutive equations that couple the pressure-strain and momentum-velocity relationships. This coupling arises from subwavelength asymmetry and non-locality in heterogeneous media. This paper…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
In this article: a) a method is developed for calculating volumetric diagrams of elastic scattering of microparticles (in particular, electrons and photons) on single-layer and multi-layer statistically uneven surfaces; b) the diffraction…
The goal of this work is to determine classes of traveling Solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.