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The possibility of heavy ion additional acceleration in laser beams is investigated. The main observation is the existence of a big variety of acceleration modes due to many fitting parameters even for only one Gaussian beam and for crossed ones even more so. An essentially non-monotonic dependence of energy gain on relevant variables such as initial velocity or pulse duration is found which makes the search for the most effective acceleration modus very complex. There is a threshold level for the intensity (» 1025W/cm2) when the ion moves in the capture mode in one direction.

Population dynamics of highly excited states of a hydrogen atom under the action of an ultra-short intense laser pulse is studied by means of direct numerical solution of  Schr¨ edinger equation in the finite basis of eigenstates of the discrete and continuous energy spectrum. The essential role of continuous spectrum states is demonstrated. Formation of localized wave packets of Rydberg states is discussed.

The dynamics of populations of 4s and 3p states in hydrogen atom is investigated under the action of ultra high laser single frequency linear-polarized pulse at one-, two- and three-photon resonance and at large detuning out of frame of perturbation theory and rotating wave approximation. It was shown the existence of low frequency modulation of optical oscillations,which frequency becomes zero at some values of laser field amplitude.

Fully vectorial plane wave method is presented aimed the calculation of the electromagnetic eigenwaves in periodical dielectric media having arbitrary geometry and dimension with both isotropic and anisotropic elements. Using this method the effect of the reorientation of molecules of anisotropic material in photonic crystal on the dispersion surface is investigated.

The results of numerical modelling of the supercontinuum generation in microstructure fibers excited by femtosecond multi-soliton pulses are presented. Pulse dynamics is modelled using the extended Schrodinger equation, in which the dispersion and nonlinear coefficient for given fiber are calculated by plane wave method. It is more easy to achieve the phase-matching conditions for the dispersive wave generation in the fibers with periodical modulated diameter.

Results of experimental research of synchronization of two coupled almost identical resonance microwave active oscillators on multicavity klystrons in the modes of periodic and chaotic oscillations are presented. It is shown that depending on type of coupling it is possible to realize a mode of mutual frequency capture, synchronization by means of chaos full elimination by outer harmonic signal, and full synchronization mode. A possibility of using the chaos elimination effect for generation of sequence of chaotic radio pulses is shown.

In the work a new model of a continuous active medium with unidirectional coupling of active elements is proposed. The Anishchenko–Astakhov oscillator was selected as an active element. The model shows both regular and chaotic in time regimes. The results  obtained for the medium are compared with the results for a chain of Anishchenko–Astakhov oscillators. The problem of conformity between the discrete model and the continuous medium is analyzed.

A phase synchronization coefficient estimate, obtained from a time series, can take a high value even for uncoupled oscillators in the case of short signals and close basic frequencies. Since such situations are widespread in practice, it is necessary to detect them to avoid false conclusions about the presence of coupling. We investigate statistical properties of the estimator with the use of an exemplary system – uncoupled phase oscillators. Conditions leading to high probability to get big values of the estimator are determined quantitatively.

The numerical scheme for calculation the set of Lyapunov exponents in distributed systems with delayed feedback based on a modification of Benettine algorithm is described. The results of numerical simulation of two such systems (active oscillator with cubic nonlinearity and active oscillator of klystron type) are presented. The sets of Lyapunov exponents in different regimes, particularly in regimes of «weak» and «developed» chaos are analyzed. The calculation peculiarities of the set of Lyapunov exponents in the systems with delayed feedback are discussed.

In present paper we study the effect of synchronization of two-frequency quasiperiodic oscillations. We analyze both external and mutual synchronization. The peculiarities of synchronization of a resonant limit cycle on a two-dimensional torus are established. It is shown that in general case, one and then another one of the basic frequencies is locked. The results of computer simulation are confirmed experimentally.