Метод автоматического планирования траектории беспилотного летательного аппарата в условиях ограничений на динамику полета
In the frame of the third-order nonlinear wave dispersion theory the equation of motion of a vector wave packets mass center taken in to account arbitrary inhomogeneity profile is obtained. As short vector wave packets localized motion as infinite motion is shown. Short vector wave packets localizations area can be as bigger as smaller in comparison with long vector wave packets localizations area. The effect depend from third-order linear dispersion parameter.
Propagation of the short vector envelope solitons in a inhomogeneous medium with linear potential in coupled third–order nonlinear Shrodinger equations frame is considered. Explicit vector soliton solution is obtained. The explicit solution for the solitons trajectories is studied. In particular cases this solitons solution can be reduced as to the short scalar soliton solution on linear inhomogeneity profile, as to well – known Chen soliton solution.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.