Particular periodic solutions to a nonintegrable system of Schrödinger nonlinear equations and their eigenvalues

Particular solutions to the general case of a nonintegrable system of Schrödinger nonlinear equations in the form of a family of cnoidal waves are found on the assumption of linear relationship between the squared moduli of the orthogonal components of a vector field. The domains of existence of solutions and the corresponding spectra of eigenvalues are determined.     

“Magnetodipole” self-organization of charge carriers in high-T c superconductors and the kinetics of phase transition

A phenomenological model describing “magnetodipole” self-organization of charge carriers (the formation of so-called stripe-structures and the energy gap in the spectrum of states) was suggested to interpret the data of nonstationary nonlinear spectroscopy of high-T _c superconductors. It was shown that, after rapidly heating a superconducting sample, the kinetics of the succeeding phase transition depended on initial temperature T. At small “overheatings” T*<T<T _m x≈(1.4?1.5)T* (T _c and T*≈T _c are the temperatures of the transition to the superconducting state and the formation of stripe-structures) and the optimal level of doping, the decay of stripe-structures (and of the gap in the spectrum of states) occurred at a low rate (in times above to 10^?9 s) in spite of the virtually instantaneous disappearance of superconductivity.     

Low-frequency dispersion of fundamental waves in anisotropic piezoelectric plates

Low-frequency onset of the fundamental branches in piezoplates is studied with a view to identify the impact of piezoelectric coupling. General analytical expressions for the zero- and leading-order terms of the velocity versus wavenumber expansion in an anisotropic homogeneous piezoplate are obtained. On this ground, it is shown what types of anisotropy and electric boundary conditions enable the onset parameters of fundamental branches to be piezoactive. Particular attention is given to the linear dispersion at the origin of two upper fundamental branches. This property is entirely caused by the piezoeffect, being ruled out for elastic plates. An invariant hierarchy is established between the zero-order velocities of the fundamental waves under different electric boundary conditions in homogeneous and functionally graded plates. It is shown that some of these velocities in a metallized plate become piezoactive specifically if the piezoplate is functionally graded.     

Anomalous behavior of the velocity of hypersonic acoustic phonons in (NH<Subscript>4</Subscript>)<Subscript>3</Subscript> H(SO<Subscript>4</Subscript>)<Subscript>2</Subscript> crystals

The Gross-Pitaevski equation modified through the inclusion of a term accounting for the nonlocality of interatomic interaction was used to demonstrate the occurrence of extremely narrow two-and three-dimensional solitonic states in atomic Bose-Einstein condensates. The estimates of the sizes of these states gave a value of ～ 20–60 nm (atomic “needles” and “bullets”) for lithium atoms. The soliton lifetimes caused by two-and three-particle collisions were estimated. The limiting possibilities of the formation of nanostructures using needles and bullets were compared with the possibilities of other nanolithographic methods.     

Growth of Er2(SO4)3 ⋅ 8H2O crystals and study of their structure and properties

New crystals of the composition Er₂(SO₄)₃ ? 8H₂O have been synthesized by the method similar to that used for synthesis of (CH₃)₂NH₂Al(SO₄)₂ ? 6H₂O. The synthesized crystals were studied by the X-ray diffraction method. The crystals are monoclinic C2/c) and contain no (CH₃)₂NH₂ ions. It is established that, contrary to DMAAS crystals, Er₂(SO₄)₃ ? 8H₂O crystals undergo no phase transitions and possess neither ferroelectric nor ferroelastic properties.     

Dynamic interaction of a magnetized solid body with a rarefied plasma flow

Dependences of the drag and lift coefficients of a magnetized sphere in a hypersonic rarefied plasma flow on the angle between the plasma flow velocity and the self-magnetic field induction vector of the body are obtained in a wide range of the ratio of the magnetic pressure to the plasma flow pressure. It is shown that changing the orientation of the magnetic field vector of the body and the incoming flow velocity can be used to control the dynamic interaction in the plasma–body system, namely, to decelerate and accelerate the magnetized sphere in a rarefied hypersonic plasma flow.