Showing papers by "Vladimir E. Zakharov published in 1996"
TL;DR: In this article, the authors combine the canonical formalism for free-surface hydrodynamics and conformal mapping to the half-plane to obtain a simple system of pseudo-differential equations for the surface shape and hydrodynamic potential.
208 citations
TL;DR: A numerical model based on the expansion of the Hamiltonian of the surface up to terms of fourth order observes the formation of powerlike spectrum of spatial elevations close to one predicted by weak-turbulent theory.
Abstract: A numerical model for direct simulation of the surface of ideal fluid based on the expansion of theHamiltonian of the surface up to terms of fourth order is developed. For the case of capillary wavewe observe the formation of powerlike spectrum of spatial elevations close to one predicted by weak-turbulent theory
125 citations
Journal Article•
107 citations
01 Jan 1996
TL;DR: In this paper, the problem of the asymptotic behavior of an arbitrary initial condition is in this way far from exhausted; it is still necessary to determine the non-soliton part of the solution which is connected with the continuous spectrum of the corresponding differential operator.
Abstract: Recently it has been established that a whole number of non-linear wave equations of importance to physics can be integrated exactly by means of a new mathematical method-the inverse scattering method. Among those we have the Korteweg-de Vries equation, tl] the non-linear Schrodinger equation, [2,3] the Sine-Gordon equation, [4.5] and others. The formalism of the inverse method enables us to find easily extensive classes of exact solutions which describe the propagation and interaction of solitary waves-solitons, and to determine their asymptotic behavior. [2,3,6-8] However, the problem of the asymptotic behavior of an arbitrary initial condition is in this way far from exhausted; it is still necessary to determine the asymptotic behavior of the "non-soliton" part of the solution which is connected with the continuous spectrum of the corresponding differential operator. 1l The present paper is devoted to the solution of that problem.
36 citations
TL;DR: Using the combination of the canonical formalism and conformal mapping, a theory of the free surface of deep water in the approximation of a high curvature is developed in this paper.
13 citations
TL;DR: In this article, a numerical model of the high-latitude ionospheric electric field is presented and the electric field patterns are calculated consistently both in the northern and southern hemispheres.
Abstract: A numerical model of the high-latitude ionospheric electric field is presented. To perform the calculations, a model of the field-aligned current source is proposed. The electric field patterns are calculated consistently both in the northern and southern hemispheres. Effects of season, universal time, solar and geomagnetic activity, the neutral atmosphere winds, and of the IMF sector structure are considered. In particular, dynamics of the parameters of convection cells are investigated that depend on the action of these factors. Comparison of the results with experimental data is carried out.
5 citations
01 Jan 1996
4 citations