The article establishes that Euler’s problem of two attractive centres contains another conservation law alongside with the energy conservation
one, which is also quadratic in velocities. These conservation laws and elliptic coordinates considerably simplify the procedure of trajectory equations generation.
The article uses the method of spatial point reflection for the definition of complex potentials of filtrational flows in an area limited by
rectangle. The article considers possible conditions and generates solutions in the form of infinite series. For point source the series are presented by means of the Jacobi theta-function or the Weierstrass sigmafunction.
The article considers the interaction of a two-dimensional anticyclone with a barrier and generates and solves its motion equation. The
authors claim that an anticyclone accelerates at the approach of the edge of a barrier forming an intensive stream. The article also offers
the streamline pattern analysis.
The article offers a new method of obtaining multisoliton solutions of KdV equations by means of introducing the characteristic polynomial.
The authors form a representation for multisoliton solutions through the second logarithmic derivative of a determinant of a positive-definite matrix.
The article shows that the Lindblad Master Equation for finitedimensional Hilbert space can be presented as a Schrödinger Equation on a Hilbert space of greater dimension. This equation can be considered as an equation of the evolution of an integrated system consisting of two subsystems: observational and auxiliary ones. This equation allows solutions in the form of entangled states.
The article analyses scattering problem for a ground penetrating radar and presents a test on the basis of ground penetrating radar system
signals for several underground objects.
The article focuses on the possibilities of physical interpretation of global ionosphere agitations in the period of elevated geomagnetic activity.
The authors offer a physical interpretation of this phenomenon based on the assumption about the agitation of planetary Poincare waves in atmosphere. The analysis of the space-time structure of these waves gives a credible explanation of the ionospheric dynamics under observation.
The article considers the real analog of the Schrodinger nonlinear system of equations (NSE). The generated Lax pair reveals to be an invariant
for Schlesinger transformation, with the help of which a set of solutions expressed through Viète type polynomials has been founded.
The article examines the deduction and the scope of the equation describing the dynamics of a thin layer of liquid over inclined bottom
in the framework of Eckman’s approach and obtains exact solutions in the form of travelling waves. The author makes a conclusion this equation
is non-integrable on the basis of Painlevé analysis.
The article offers the deduction of expressions for the Greene function of the Dirichlet problem for a strip and a rectangle by means of
three methods: the Fourier method and methods involving the factorized variant of the symmetry principle and conform maps.