Explicit breather solution of the nonlinear Schrödinger equation

Theoretical and Mathematical Physics - We present a one-line closed-form expression for the three-parameter breather of the nonlinear Schrödinger equation. This provides an analytic proof of...     

Operator Interpolation and Systems of Linear Equations and Inequalities in Euclidean Spaces

Ukrainian Mathematical Journal - We establish new criteria of compatibility for a linear system of equations (equivalent to the Kronecker–Capelli theorem) or inequalities (equivalent to the...     

A Variational Finite Element Discretization of Compressible Flow

Foundations of Computational Mathematics - We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure-preserving way,...     

Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

Journal of Fourier Analysis and Applications - We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( $$SG$$ ), which is a fractal set that can be viewed as a limit...     

Crystallographic Parameters of Special Grain Boundaries in Multicrystalline Silicon

Crystallography Reports - The orientation of grains and the special boundaries formed by them in multicrystalline silicon has been studied by electron backscattered diffraction. It is found that...     

Neutron Spectroscopy: The Initial Steps of Development in Our Country and Several Achievements

Crystallography Reports - Some questions related to the establishment, development, and prospects of physical studies using inelastic thermal-neutron scattering are briefly reviewed. The directions...     

Fractional derivative method for describing solitons on the surface of deep water

Theoretical and Mathematical Physics - The fractional derivative method is used to take wave dispersion into account in the wave equation when describing the propagation of gravitational soliton...     

Polycrystallinity in Gallium Arsenide Crystals Grown by the Czochralski Method

Crystallography Reports - The specific features of the formation of crystallites in gallium arsenide crystals grown by the Czochralski method have been investigated. The crystallites are found to...     

Methods of Coherent X-Ray Diffraction Imaging

Crystallography Reports - Methods of coherent X-ray diffraction imaging of the spatial structure of noncrystalline objects and nanocrystals (nanostructures) are considered. Particular attention is...     

One-sided invertibility of discrete operators with bounded coefficients

Aequationes mathematicae - For $$p\in (1,\infty )$$ , we establish several criteria of one-sided invertibility on spaces $$l^p=l^p(\mathbb {Z})$$ for discrete band-dominated operators being either...