相关论文: Solution of the nonrelativistic wave equation in t…

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…

In this paper we establish optimal pointwise decay estimates for non-dispersive (compact) radial solutions to non-linear wave equations in 3 dimensions, in the energy supercritical range. As an application, we show for the full energy…

In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…

Solutions to the wave equation with constant coefficients in $\mathbb{R}^d$ can be represented explicitly in Fourier space. We investigate a reconstruction formula, which provides an approximation of solutions $u(.,t)$ to initial data…

By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of…

In this article we discuss the long-time dynamics of the radial solutions to the energy-critical wave equation in 3-dimensional space. Given a solution defined for all time $t\geq 0$, we show that the soliton resolution phenomenon happens…

In this paper, we use the variational method to find the normalized solutions of the quadratic coupled three wave Schrodinger equation with asymmetric coercive potential. We prove the existence of solutions for the system with 2-norm…

This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…

Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…

Equilateral triangular waveguides are one of the very few special kind of waveguides, whose field solutions can be constructed without necessarily solving the Maxwell's equations. Solutions can be obtained simply by superposing some plane…

Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We…

We study nonsymmetric tridiagonal operators acting in the Hilbert space $\ell^2$ and describe the spectrum and the resolvent set of such operators in terms of a continued fraction related to the resolvent. In this way we establish a…

The Faddeev equations for the three body bound state are solved directly as three dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three body binding…

We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…

We study rotating wave solutions of the nonlinear wave equation $$ \left\{ \begin{aligned} \partial_{t}^2 v - \Delta v + m v & = |v|^{p-2} v \quad && \text{in $\mathbb{R} \times \mathbf{B}$} \\ v & = 0 && \text{on $\mathbb{R} \times…

Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semi-discretization in time with these integrators is shown for a sufficiently regular…

This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…

We find solutions for a linear deformation of the symmetric three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is…

A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…

The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…