Dromion perturbation for the Davey-Stewartson-1 equations

The perturbation of the dromion of the Davey-Stewartson-1 equation is studied over the large time

Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point

The Dirichlet problem for the heat equation in a bounded domain G⊂Rn+1 is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t=c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii’s paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.Задача Діріхлє для рівняння тєплопровідності в обмеженій області G⊂Rn+1 є характеристичною, оскільки існують граничні точки, в яких границя є дотичною до характеристичної гіперплощини t=c, де c є сталою. I. Г. Петров-ський (1934) уперше встановив необхідні та достатні умови на границю, що гарантують неперервність розв'язку аж до характеристичної точки за умови, що дані Діріхле є неперервними. Поява даної роботи була викликана постійним інтересом до вивчення загальних граничних задач для рівнянь параболічного типу в обмежених областях. Наш внесок у вивчення цієї проблеми полягає в побудові формального розв'язку задачі Діріхле для рівняння теплопровідності в околі гострокінцевої характеристичної граничної точки та дослідженні його асимптотичного характеру

Comparison of dynamic of autonomic control indices in cardiovascular system under the treatment by ACE inhibitor (Enalapril) and beta-blocker (Metoprolol) in patients with hypertension

The objective of the present research was to compare the influence of Enalapril and Metoprolol on synchronization of 0.1 Hz-regulation of heart and blood microcirculation. 42 patients aged 49±9 years old with hypertension I, II were included in the study. 0.1 Hz-oscillations in heart rate variability (HRV) and blood microcirculation were registered during the passive orthostatic sign while breathing spontaneously. The duration of each test was 10 minutes. Synchronization was estimated as a phase difference between 0.1 Hz-rhythms in heart rate and in filling of blood microcirculation. Quantitative measures of synchronization were also estimated. In addition frequency values of HRV spectrum in LF- and HF-ranges were assessed. Enalapril and Metoprolol had comparable effect on blood pressure reduction. Treatment with both Enalapril and Metoprolol in patients with significant vegetative dysfunction resulted in repair of functional interaction between 0.1 Hz-regulation of heart and blood microcirculation. Enalapril was preferred in hypertensive patients with prevalence of disorders of vegetative regulation of blood microcirculation. Metoprolol influenced positively on 0,1 Hz-rhythm synchronization in patients with predominance of heart vegetative regulation dysfunction and in patients with sympathicotonia. In patients with hypertension and initially normal level of synchronization of 0.1 Hz-mechanisms treatment with Enalapril or Metoprolol caused functional dissociation. Differentiated approach to the choice of hypertensive therapy should consider individual peculiarities of system vegetative dysfunction. The level of synchronization of 0.1 Hz-rhythms in cardiovascular system should especially be evaluated initially and during the treatmen

Solitons in Triangular and Honeycomb Dynamical Lattices with the Cubic Nonlinearity

We study the existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the fundamental strongly localized soliton, the results depend on the coordination number, i.e., on the particular type of the lattice. The long-range interactions additionally destabilize the discrete soliton, or make it more stable, if the sign of the interaction is, respectively, the same as or opposite to the sign of the short-range interaction. We also explore more complicated solutions, such as twisted localized modes (TLM's) and solutions carrying multiple topological charge (vortices) that are specific to the triangular and honeycomb lattices. In the cases when such vortices are unstable, direct simulations demonstrate that they turn into zero-vorticity fundamental solitons.Comment: 17 pages, 13 figures, Phys. Rev.

Excitation of Pi3 Type Pulsations during Substorm

Two types of long-period geomagnetic pulsations within the Pi3 range (Pip and Ps6) are examined by the comparative analysis of their properties and their places in the development of substorms at high latitudes. Based on various properties differing between Pip and Ps6 pulsations which are clarified in the present paper, it is concluded that these pulsations are accompanied by different types of waves in the magnetosphere and have different generation mechanisms