A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy

In the present paper we begin studies on the large time asymptotic behavior for solutions of the Cauchy problem for the Novikov--Veselov equation (an analog of KdV in 2 + 1 dimensions) at positive energy. In addition, we are focused on a family of reflectionless (transparent) potentials parameterized by a function of two variables. In particular, we show that there are no isolated soliton type waves in the large time asymptotics for these solutions in contrast with well-known large time asymptotics for solutions of the KdV equation with reflectionless initial data

A RARE CASE OF ALVEOLAR SARCOMA OF THE PARAPHARYNGEAL SPACE

The paper describes the rare malignancy alveolar soft tissue sarcoma. The tumor was located in the parapharyngeal space; it was detected during pregnancy. The authors give the data available in the literature on the clinical manifestations of this disease, the specific features of morphological diagnosis, and treatment policy. The described case focuses on the complexities of diagnosis and preoperative preparation and surgical techniques

Topological Phenomena in the Real Periodic Sine-Gordon Theory

The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the consequences of this property. In particular this description allows to calculate the topological charge of solutions (the averaging of the $x$-derivative of the potential) and to show that the averaging of other standard conservation laws is the same for all components.Comment: LaTeX, 18 pages, 3 figure

On the equivalence of different approaches for generating multisoliton solutions of the KPII equation

The unexpectedly rich structure of the multisoliton solutions of the KPII equation has been explored by using different approaches, running from dressing method to twisting transformations and to the tau-function formulation. All these approaches proved to be useful in order to display different properties of these solutions and their related Jost solutions. The aim of this paper is to establish the explicit formulae relating all these approaches. In addition some hidden invariance properties of these multisoliton solutions are discussed

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.Comment: 15 page

Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

ВЕРОЯТНОСТНО-СТАТИСТИЧЕСКАЯ ОЦЕНКА ШЕРОХОВАТОСТИ ПОВЕРХНОСТИ ЭЛЕКТРОИМПУЛЬСНО ПОЛИРОВАННЫХ ДЕТАЛЕЙ

The paper presents methodology and results of investigations pertaining to profilograms of specimen surfaces being polished using electric pulse method and being made of steel 10 и 20Х13 with the help of correlative transformation. It has been established that in the process of polishing topography formation is initiated due to simultaneous surfacing of micro- and sub-micro-irregularities with equal probability and equal intensity. The obtained mechanism for topography formation is justified by the fact that break-down of gas-vapor shell takes place with equal probability as on the micro-profile top so in its cavities on the polished surface in the zones of accidental  non-homogeneity of electric field.Приведены методика и результаты исследования профилограмм электроимпульсно полированных поверхностей образцов из сталей 10 и 20Х13 с помощью корреляционного преобразования. Установлено, что в процессе полирования формирование топографии поверхности происходит за счет одновременного с равной вероятностью и равной интенсивностью сглаживания микро- и субмикронеровностей поверхности. Выявленный механизм формирования топографии обусловлен тем, что пробой парогазовой оболочки происходит с равной вероятностью как на вершинах, так и во впадинах микропрофиля обрабатываемой поверхности в областях случайных неоднородностей электрического поля.

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

Gradient catastrophe and flutter in vortex filament dynamics

Gradient catastrophe and flutter instability in the motion of vortex filament within the localized induction approximation are analyzed. It is shown that the origin if this phenomenon is in the gradient catastrophe for the dispersionless Da Rios system which describes motion of filament with slow varying curvature and torsion. Geometrically this catastrophe manifests as a rapid oscillation of a filament curve in a point that resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painlev\'e-I equation.Comment: 11 pages, 3 figures, typos corrected, references adde

Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface

We consider the dimensional crossover in the topological matter, which involves the transformation of different types of topologically protected zeroes in the fermionic spectrum. In the considered case, the multiple Dirac (Fermi) point in quasi 2-dimensional system evolves into the flat band on the surface of the 3-dimensional system when the number of atomic layers increases. This is accompanied by formation of the spiral nodal lines in the bulk. We also discuss the topological quantum phase transition at which the surface flat band shrinks and changes its chirality, while the nodal spiral changes its helicity.Comment: 13 pages, 7 figure