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The generation of Raman solitons in the mid-IR range in a multicore fiber with two zero-dispersion wavelengths is studied analytically and numerically. The estimate for the maximum shift of the Raman soliton wavelength depending on the parameters of the media dispersion, the frequency-dependent losses, and the nonlinearity decreasing is obtained, which is in good agreement with the results of numerical simulation. A realistic design of a 10-core fiber made of a pair of compatible glasses is proposed for the Raman shift of the wavelength of soliton pulses propagating in an out-of-phase mode. The nonlinear dynamics of a laser pulse, specified at the wavelength of $2.3\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$, energy of 1.5 nJ, and duration of 100 fs, during propagation in a fiber with this design, is studied numerically. The generation of Raman solitons in the mid-IR range at wavelengths exceeding $4\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$, as well as dispersion waves in the $5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$ range, emitted by a soliton when approaching the second zero-dispersion wavelength, is demonstrated.

An equation is derived for analyzing the self-action of a wave packets with few optical cycles in multicore fibers (MCF). A new class of stable out-of-phase spatio-temporal solitons with few cycle durations in the MCF with cores located in a ring is found and analyzed. The stability boundary of the obtained solutions is determined. As an example of using such solitons, we considered the problem of their self-compression in the process of multisoliton dynamics in the MCF. The formation of laser pulses with a duration of few optical cycles at the output of a ten-core MCF is shown.

The method of the laser pulse self-compression in the process of noise-seeded Raman scattering in a plasma created by a counterpropagating ionized pulse is considered. The sharpness of the ionization front ensures the formation of an output pulse close to the $\ensuremath{\pi}$-pulse solution with a sharp leading edge. The dependence of the gain increment on the transverse wave number leads to the formation of a smooth phase front of the output pulse. The energy efficiency in the output pulse reaches 28% of the total pump energy. A study of the influence of quasistatic inhomogeneities showed only a slight slowdown in the process, even in a plasma with 8% density modulation.

The propagation of laser pulses in multicore fibers (MCFs) made of a central core and an even number of cores located in a ring around it is studied. Approximate quasisoliton homogeneous solutions of the wave field in the MCF considered are found. The stability of the in-phase soliton distribution is shown analytically and numerically. At low energies, its wave field is distributed over all MCF cores and has a duration that exceeds the duration of the nonlinear Schr\"odinger equation (NSE) soliton with the same energy by many (i.e., five to six) times. In contrast, almost all of the radiation at high energies is concentrated in the central core with a duration similar to the NSE soliton. The transition between the two types of distributions is very sharp and occurs at a critical energy, which is weakly dependent on the number of cores and on the coupling coefficient with the central core. The self-compression mechanism of laser pulses was proposed. It consists in injecting such MCFs with a wave packet being similar to the found soliton and having an energy larger than the critical value. It is shown that the compression ratio depends weakly on the energy and the number of cores and is approximately equal to six times with an energy efficiency of almost 100%. The use of longer laser pulses allows one to increase the compression ratio up to 30--40 times with an energy efficiency of more than 50%. The obtained analytical estimates of the compression ratio and its efficiency are in good agreement with the results of a numerical simulation.

The features of the self-action of a wave field in a small-sized optical system consisting of $2N$ identical light guides, which are disposed equidistantly along a ring, and an isolated fiber in the center are studied analytically and numerically. Stable exact solutions are found for intense wave beams in such a system, allowing long-distance coherent transport of radiation in a set of optical fibers. The total beam power in this case can exceed several times the critical power of self-focusing in the continuous medium. This is clearly manifested for the out-of-phase spatial distribution of ${u}_{n}={(\ensuremath{-}1)}^{n}f$, which is stable at arbitrary powers. Direct numerical simulation of the nonlinear unidirectional wave propagation equation confirms the stability of found wave field distributions.

The analytical and numerical study of the radiation self-action in a system of coupled light guides is fulfilled on the basis of the discrete nonlinear Schr\"odinger equation (DNSE). We develop a variational method for qualitative study of DNSE and classify self-action modes. We show that the diffraction of narrow (in grating scale) wave beams weakens in discrete media and, consequently, the ``collapse'' of the one-dimensional wave field with power exceeding the critical value occurs. This results in the ability to self-channel radiation in the central fiber. Qualitative analytical results were confirmed by numerical simulation of DNSE, which also shows the stability of the collapse mode.

We show that a self-focusing mode for intense laser pulses comprising less than about ten optical cycles is resistant to the transverse modulational instability. For such pulses, a method of pulse self-compression based on adiabatic decrease of the duration of a solitonlike wave packet and transverse cumulating of energy during the self-focusing in Kerr-like media with anomalous dispersion is proposed. This method can be used for generation of high-quality, high-energy, few-cycle pulses down to a single-cycle duration.

A regime of extreme self-compression of optical solitons to single-cycle duration with further shortening along with superbroad spectrum up-shifting is revealed when the Kerr nonlinearity and ionization process are independently controlled. This results in efficient optical-pulse compression as a whole towards extremely short single-cycle pulses at essentially shorter wavelengths, which may open a new way to generate optical pulses with durations of hundreds of attoseconds in the ultraviolet domain.

A detailed theoretical investigation is performed for the self-compression of relativistically strong laser pulses under plasma wake wave excitation conditions. An analytical expression is obtained for the characteristic length of laser pulse self-compression in the one-dimensional case. A good agreement between the theoretical and numerical calculation of the dependence of the wave-packet compression length on both amplitude and plasma concentration is demonstrated. The influence of the wave beam self-focusing radiation process on the rate of shortening of the laser pulse duration is considered.

We propose the concept of a plasma compressor capable of producing extremely short relativistic laser pulse, which is based on the studies of self-focusing of high-power laser pulses under the wake-wave excitation conditions. It is shown that, in the optimal regime, the compression of laser pulses up to a duration of one optical cycle is possible. We study the influence of hose instability on the process of pulse self-compression and have found that this instability is not important for a wide set of initial conditions. The matter is that the length of pulse distortion in both transverse and longitudinal directions is larger than the length of the pulse self-compression. Hose instability gives only negligible decrease of compression degree and weak deformation of pulse profile.

We present experimental results for laser pulse compression due to wakefield excitation in the relativistic regime using the spectral phase interferometry for direct electric-field reconstruction technique for complete pulse characterization. The results indicate that the pulse was compressed to a 10-fs duration which was verified by fully relativistic three-dimensional particle-in-cell simulations. Optimized modeling based on a hydrodynamic code was also done, showing the possibility of producing laser pulses of few-cycle duration.

We present a class of few-cycle elliptically polarized solitary waves in an isotropic Kerr medium. It is proved numerically that they are stable and can be easily excited during pulse propagation. We also propose a method of producing multisolitons with different polarization states and study their binary collisions. It is shown that collisional properties strongly depend on their relative polarization rotation.

In a transparent medium with instantaneous Kerr nonlinearity we find a new class of few-optical-cycle solitons and prove them to be the fundamental structures in pulse propagation dynamics. We demonstrate numerically that in the asymptotic stage of pulse propagation the input pulse splits into isolated few-cycle solitons where the quantity and their parameters are determined by the initial pulse. We generalize the concept of the high-order Schrödinger solitons to the few-cycle regime and show how it can be used for efficient pulse compression down to the single cycle duration.