相关论文: Colliding plane waves with W=M=0

It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence…

In the present paper, we study the following Schr\"{o}dinger-Maxwell equation with combined nonlinearities \begin{align*} \displaystyle - \Delta u+\lambda u+ \left(|x|^{-1}\ast |u|^2\right)u =|u|^{p-2}u +\mu|u|^{q-2}u\quad \text{in} \…

Rozowsky, Volkas and Wali recently found interesting numerical solutions to the field equations for a gauged U1xU1 scalar field model. Their solutions describe a reflection-symmetric domain wall with scalar fields and coupled gauge…

In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane…

In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…

An exact plane-symmetric non-stationary solution to the Einstein-Maxwell equations for a magnetoactive plasma is obtained and studied.

In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave…

A unified treatment for the propagation of classical waves in inhhomogeneous media is proposed. We deal with four kinds of waves, they are the acoustic wave in fluid, the elastic shear wave in two diemnsional solid, and the E- and…

The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics…

We consider a class of semilinear elliptic system of the form $-\Delta u(x,y)+\nabla W(u(x,y))=0,\quad (x,y)\in\R^{2}$ where $W:\R^{2}\to\R$ is a double well non negative symmetric potential. We show, via variational methods, that if the…

In this paper, we have considered how to detect the processes of plane gravitational waves colliding. The degenerate Ferrari-Ibanez solution describes the collision of plane gravitational waves with aligned linear polarization, and the…

We consider standing waves of the nonlinear Schr\"odinger equation $i\partial_t u = -\Delta_\alpha u + |u|^{p-1}u$ in the defocusing case in dimensions $N=2$ and $N=3$. Here, $-\Delta_\alpha$ denotes the Laplacian with a point interaction.…

We applied canonical transformation to water wave equation not only to remove cubic nonlinear terms but to simplify drastically fourth order terms in Hamiltonian. This transformation explicitly uses the fact of vanishing exact four waves…

We consider periodic waves in miscible two-component Bose-Einstein condensates with repulsive nonlinear interactions constants. Exact one-phase solution is found for the case when all these constants are equal to each other (i.e., for…

For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation,…

Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect…

The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…

Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) Interaction solutions between lump wave and solitary waves; (iii) Interaction solutions…

This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid (of finite depth and in irrotational motion) for…