相关论文: The Method of Ascent and cos(sqrt(A^2+b^2))
Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…
A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both…
The non-Abelian Kubo formula is derived from the kinetic theory. That expression is compared with the one obtained using the eikonal for a Chern-Simons theory. The multiple time-scale method is used to solve the non-Abelian Kubo formula,…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through…
This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen…
We propose a simple algebraic method for generating classes of traveling wave solutions for a variety of partial differential equations of current interest in nonlinear science. This procedure applies equally well to equations which may or…
We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the…
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
We present a simple way to calculate non-Gaussianity in inflation using fully non-linear equations on long wavelengths with stochastic sources to take into account the short-wavelength quantum fluctuations. Our formalism includes both…
The Bethe-Salpeter amplitude is expanded on a hyperspherical basis, thereby reducing the original 4-dimensional integral equation into an infinite set of coupled 1-dimensional ones. It is shown that this representation offers a highly…
In this paper, we solve the initial value problems of variable-coefficient generalized wave equations associated with trees and a large family of linear constant-coefficient partial differential equation by algebraic methods. Moreover, we…
In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…
A wavelike scalar-Einstein solution is found and indicating vectors constructed from the Bel-Robinson tensor are used to study which objects co-move with the wave and whether gravitational energy transfer is null.
Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in general scalar and vector nonlinear wave equations are proposed.…
Using the KAM method, we exhibit some solutions of a finite-dimensional approximation of the Zakharov Hamiltonian formulation of gravity water waves, which are spatially periodic, quasi-periodic in time, and not permanent form travelling…
A new operator equation for periodic gravity waves on water of finite depth is derived and investigated; it is equivalent to Babenko's equation considered in \cite{KD}. Both operators in the proposed equation are nonlinear and depend on the…
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite…
In this note we study solitary wave solutions of a class of Whitham-Boussinesq systems which includes the bi-directional Whitham system as a special example. The travelling wave version of the evolution system can be reduced to a single…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…