Representations for the solutions and coefficients of second-order differential equations

New representations are given for the solutions and coefficients of second-order evolution differential equations in the linear and nonlinear cases. The formulas for linear equations have wide arbitrariness which can be used in identification problems. We study the questions of running-wave type for nonlinear one-dimensional equations.     

Some questions concerning constructive methods in the theory of inverse problems

Under consideration are some questions concerning the existence of the transformations described by Yu. E. Anikonov for the second-order partial differential equations and those concerning the search of information on constructing transformations with certain conditions (for example, the divergent form of the so-obtained equation may be such a condition). Using the two-dimensional heat conductivity equation, we give examples of constructing the solutions of inverse problems.     

Twisted conjugacy classes of the unit element

We study twisted conjugacy classes of the unit element in different groups. Fel’shtyn and Troitsky showed that the twisted conjugacy class of the unit element of an abelian group is a subgroup for every automorphism. The structure is investigated of a group whose twisted conjugacy class of the unit element is a subgroup for every automorphism (inner automorphism).     

Magnetopause charging and transfer of momentum and energy into magnetosphere

The theory of charged current sheets is compared with plasma data of Prognoz-8, Interball-1, Polar, and Cluster satellites. The possibility of momentum and energy transfer into the magnetosphere, irrespective of magnetic field line reconnection, as a specific dynamo effect, is shown. This relates statistical properties of the turbulent boundary layers with the character of the transfer through thin boundaries.     

Bäcklund Transformations for the One-Dimensional Schrödinger Equation

Journal of Applied and Industrial Mathematics - We study the system of equations which bases on the one-dimensional Schrödinger equation and connects the potential, amplitude, and phase...