相关论文: Discrete transformation for matrix 3-waves problem…
In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…
The possibility of a complex 4-dimensional space-time manifold is suggested. This may imply the existence of a matter wave.
A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets…
The approach of direct integration of the three-dimensional Faddeev equations with respect to the breakup T-matrix in momentum space for three bodies of different masses is presented. The Faddeev equations are written out explicitly without…
The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin…
In previous publications, we illustrated the effectiveness of the method of the inhomogeneous differential equation in calculating the electric polarizability in the one-dimensional problem. In this paper we extend our effort to apply the…
In this short note we explain how to construct resolutions or regular alterations admitting an ample exceptional divisor, assuming the existence of projective resolutions or regular alterations. In particular, this implies the existence of…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their…
This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates,and prove that small localized data leads to global…
We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…
We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher…
In this paper we give a method to obtain Darboux transformations (DTs) of integrable equations. As an example we give a DT of the dispersive water wave equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek equation.…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
The author proposes the methodology of transformation optics in orthogonal coordinates to obtain the material parameters of the transformation media from the mapping in orthogonal coordinates. Several examples are given to show the…
We recommended consequent discrete combinatorial research in mathematical physics. Here we show an example how discretization of partial differential equations can be done and that quickly unexpected new findings can result from research in…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
Point transformations of the 3-rd order ordinary differential equations are considered. Special classes of ordinary differential equations that are invariant under the general point transformations are constructed.