Construction of a model of the Venus surface and its use in processing radar observations

An algorithm is described for constructing the model of the Venus surface as an expansion in spherical functions. The relief expansion coefficients were obtained up to the coefficient S sub 99. The surface picture representation is given according to this expansion. The surface model constructed was used for processing radar observations. The use of the surface model allows improved agreement between the design and measured values of radar ranges

Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma

We study weakly nonlinear wave perturbations propagating in a cold nonrelativistic and magnetized ideal quark-gluon plasma. We show that such perturbations can be described by the Ostrovsky equation. The derivation of this equation is presented for the baryon density perturbations. Then we show that the generalized nonlinear Schr{\"o}dinger (NLS) equation can be derived from the Ostrovsky equation for the description of quasi-harmonic wave trains. This equation is modulationally stable for the wave number $k < k_m$ and unstable for $k > k_m$, where $k_m$ is the wave number where the group velocity has a maximum. We study numerically the dynamics of initial wave packets with the different carrier wave numbers and demonstrate that depending on the initial parameters they can evolve either into the NLS envelope solitons or into dispersive wave trains

Helical solitons in vector modified Korteweg-de Vries equations

We study existence of helical solitons in the vector modified Korteweg-de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems, including plasma and chains of particles connected by elastic springs. By using the dynamical system methods such as the blow-up near singular points and the construction of invariant manifolds, we construct helical solitons by the efficient shooting method. The helical solitons arise as the result of co-dimension one bifurcation and exist along a curve in the velocity-frequency parameter plane. Examples of helical solitons are constructed numerically for the non-integrable equation and compared with exact solutions in the integrable vector mKdV equation. The stability of helical solitons with respect to small perturbations is confirmed by direct numerical simulations.Comment: 20 pages, 10 figure

The inverse problem for the Gross - Pitaevskii equation

Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first method, suggested by the work by Kondrat'ev and Miller (1966), applies to one-dimensional (1D) GPE. It is based on the similarity between the GPE and the integrable Gardner equation, all solutions of the latter equation (both stationary and nonstationary ones) generating exact solutions to the GPE, with the potential function proportional to the corresponding solutions. The second method is based on the "inverse problem" for the GPE, i.e. construction of a potential function which provides a desirable solution to the equation. Systematic results are presented for 1D and 2D cases. Both methods are illustrated by a variety of localized solutions, including solitary vortices, for both attractive and repulsive nonlinearity in the GPE. The stability of the 1D solutions is tested by direct simulations of the time-dependent GPE

Soliton spectra of random water waves in shallow basins

Interpretation of random wave field on a shallow water in terms of Fourier spectra is not adequate, when wave amplitudes are not infinitesimally small. A nonlinearity of wave fields leads to the harmonic interactions and random variation of Fourier spectra. As has been shown by Osborne and his co-authors, a more adequate analysis can be performed in terms of nonlinear modes representing cnoidal waves; a spectrum of such modes remains unchanged even in the process of nonlinear mode interactions. Here we show that there is an alternative and more simple analysis of random wave fields on shallow water, which can be presented in terms of interacting Korteweg - de Vries solitons. The data processing of random wave field is developed on the basis of inverse scattering method. The soliton component obscured in a random wave field is determined and a corresponding distribution function of number of solitons on their amplitudes is constructed. The approach developed is illustrated by means of artificially generated quasi-random wave field and applied to the real data interpretation of wind waves generated in the laboratory wind tank.Comment: 23 pages, 15 figure

Description of vortical flows of incompressible fluid in terms of quasi-potential function

It has been shown [1, 2] that a wide class of 3D motions of in- compressible viscous fluid in Cartesian coordinates can be de- scribed by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by three-component velocity field having two-component vorticity field; both these fields can depend of all three spatial variables and time, in gen- eral. Governing equations for the quasi-potential have been de- rived and simple illustrative examples of 3D flows have been presented. In this paper the concept of quasi-potential is fur- ther developed for fluid flows in cylindrical coordinates. It is shown that the introduction of a quasi-potential in curvilinear coordinates is non-trivial and may be a subject of additional restrictions. In the cases when it is possible, we construct il- lustrative examples which can be of interest for some practical applications

Motion Parameters Determination of the SC and Phobos in the Project Phobos-Grunt

The SC "Phobos-Grunt" flight is planned to 2009 in Russia with the purpose to deliver to the Earth the soil samples of the Mars satellite Phobos. The mission will pass under the following scheme [1-4]: the SC flight from the Earth to the Mars, the SC transit on the Mars satellite orbit, the motion round the Mars on the observation orbit and on the quasi-synchronous one [5], landing on Phobos, taking of a ground and start in the direction to the Earth. The implementation of complicated dynamical operations in the Phobos vicinity is foreseen by the project. The SC will be in a disturbance sphere of gravitational fields from the Sun, the Mars and the Phobos. The SC orbit determination is carried out on a totality of trajectory measurements executed from ground tracking stations and measurements of autonomous systems onboard space vehicle relatively the Phobos. As ground measurements the radio engineering measurements of range and range rate are used. There are possible as onboard optical observations of the Phobos by a television system and ranges from the SC up to the Phobos surface by laser locator. As soon as the Phobos orbit accuracy is insufficient for a solution of a problem of landing its orbit determination will be carried out together with determination of the SC orbit. Therefore the algorithms for joint improving of initial conditions of the SC and the Phobos are necessary to determine parameters of the SC relative the Phobos motion within a single dynamical motion model. After putting on the martial satellite orbit, on the Phobos observation orbit, on the quasi-synchronous orbit in the Phobos vicinity the equipment guidance and the following process of the SC orbit determination relatively Phobos requires a priori knowledge of the Phobos orbit parameters with sufficiently high precision. These parameters should be obtained beforehand using both all modern observations and historical ones