Sasa-Satsuma hierarchy of integrable evolution equations.

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms.

Spectral properties of limiting solitons in optical fibers.

It seems to be self-evident that stable optical pulses cannot be considerably shorter than a single oscillation of the carrier field. From the mathematical point of view the solitary solutions of pulse propagation equations should loose stability or demonstrate some kind of singular behavior. Typically, an unphysical cusp develops at the soliton top, preventing the soliton from being too short.

[Development of technology for the substance of poly[3-(3,4-dihydroxyphenyl) glyceric acid] from Symphytum asperum].

Comfrey (Symphytum L.) is used to treat bone fractures, tendon injuries, ulcer lesions of gastrointestinal tract. It promotes wound healing, accelerates exudates resorption in lungs and reduces joints' inflammation.

Controlling light by light with an optical event horizon.

A novel concept for an all-optical transistor is proposed and verified numerically. This concept relies on cross-phase modulation between a signal and a control pulse. Other than previous approaches, the interaction length is extended by temporally locking control and the signal pulse in an optical event horizon, enabling continuous modification of the central wavelength, energy, and duration of a signal pulse by an up to sevenfold weaker control pulse.

Breathing dissipative solitons in three-component reaction-diffusion system.

We investigate the stability of the localized stationary solutions of a three-component reaction-diffusion system with one activator and two inhibitors. A change of the time constants of the inhibitors can lead to a destabilization of the stationary solution. The special case we are interested in is that the breathing mode becomes unstable first and the stationary dissipative soliton undergoes a bifurcation from a stationary to a "breathing" state.

Measurement and 3D simulation of self-organized filaments in a barrier discharge.

We report on pattern formation phenomena in the filamentary dielectric barrier discharge between plane glass electrodes. It is for the first time that a three-dimensional (3D) self-organized glow pattern was both observed in an actual experiment and directly calculated in a full 3D discharge simulation in a quantitative manner. Specifically, we investigate the genesis of periodic patterns during the first breakdowns.

Ionization fronts in planar dc discharge systems with high-ohmic electrode.

Electric breakdown and ionization fronts are considered theoretically in a sandwich-like dc discharge system consisting of two plane-parallel electrodes and a gaseous gap in between. The key system feature is a high-ohmic cathode opposite to an ordinary metal anode. Such systems have received much attention from experimental studies because they naturally support current patterns.

Role of surface charges in dc gas-discharge systems with high-ohmic electrodes.

Surface charge of the electrodes is investigated for planar dc gas-discharge systems. Both analytical estimates and experimental data show that such a charge plays an important role for the dc systems with a high-ohmic electrode. This is demonstrated by several experiments concerning discharge establishment and pattern formation phenomena.

Nonuniform non-neutral plasma in a trap.

An analytical model for breathing oscillations in a nonuniform non-neutral plasma slab is developed. The plasma is relatively small and warm with the smallest dimension only of several Debye lengths. Nonuniformity in the equilibrium results in a frequency shift associated with pressure and boundary effects.

Nonlinear standing waves in bounded plasmas.

An analytical model for nonlinear volume oscillations in a bounded cold plasma is developed. Although here the familiar propagating wave solutions do not exist, exact nonlinear standing waves subject to appropriate boundary conditions can nevertheless be found. The behaviors of the electrons and ions are described self-consistently in terms of Lagrangian variables.

Non-neutral plasma column in an asymmetric trapping field.

A non-neutral plasma column in an asymmetric trapping field is considered in this paper. It is shown that nonlinearly interacting bulk plasma oscillations and quadrupole surface waves allow an exact analytical description. The absence of symmetry leads to nonintegrability and other nonlinear phenomena, such as passage through different resonances and phase locking.