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A nonlinear wave equation that describes different nonlinear effects in various fields of research was considered. In two particular cases, this equation was reduced to the Sine-Gordon equation and the Born-Infeld equation. Using the slowly…
A theory of optical nonresonance vector pulsing solitons in a Kerr media is considered. By using the perturbative reduction method the wave equation is transformed to the coupled nonlinear Schrodinger equations. The profile of the optical…
We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two-component extension of the one-dimensional focusing nonlinear Schrodinger equation -- the…
We show that the recently demonstrated technique for generating stationary pulses of light [Nature {\bf 426}, 638 (2003)] can be extended to localize optical pulses in all three spatial dimensions in a resonant atomic medium. This method…
In this review, a more general theory of self-induced transparency (SIT) in comparison with the theory of McCall and Hahn is considered. Using the recently developed generalized perturbative reduction method (GPRM) the SIT equations are…
Semiclassical methods are used to study the nonlinear interaction of light in vacuum in the context of four wave mixing. This study is motivated by a desire to investigate the possibility of using recently developed powerful ultrashort…
We present an analytical approach to the theory of nonlinear propagation of femtosecond optical pulses with broad-band spectrum in gases. The vector character of the nonlinear third-order polarization is investigated in details, taking into…
The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary…
Semiclassical methods are used to study the nonlinear interaction of light in vacuum in the context of four wave mixing. This study is motivated by a desire to investigate the possibility of using recently developed powerful ultrashort…
A theory of an optical vector pulsing soliton of self-induced transparency in an ensemble of semiconductor quantum dots is investigated. It is shown that a distribution of the excitonic ground-state transition dipole moments of the quantum…
Using the generalized perturbation reduction method the scalar nonlinear Schr\"odinger equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. A solution in the form of a two-component vector…
To add the detailed information to the existed knowledge of nonlinear optics field, the nonlinear optical processes of the second and third order have been discussed in their respective susceptibility tensors in the presence of degenerate…
The general form of the cubic Boussinesq-type equation is considered. In special cases, this equation is reduced to the three different versions of the cubic Boussinesq equations and also the generalized modified cubic Boussinesq equation.…
Mutual interaction of localized nonlinear waves, e.g. solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. In this research report, we report on the observation of a novel type…
We have investigated the nonlinear amplitude vector equation governing the evolution of optical pulses in optical and UV region. We are normalizing this equation for the cases of different and equal transverse and longitudinal size of…
Nonlinear effects in pulse propagation through a medium consisting of four-level double-$\Lambda$-type systems are studied theoretically. We apply three continous-wave driving fields and a pulsed probe field such that they form a closed…
We report the experimental observation of a cross-Kerr nonlinearity in a free-space medium based on resonantly-excited, interacting Rydberg atoms and electromagnetically induced transparency. The nonlinearity is used to implement…
The applied method of slowly varying amplitudes of the electrical and magnet vector fields give us the possibility to reduce the nonlinear vector integro-differential wave equation to the amplitude vector nonlinear differential equations.…
Specific features of nonlinear interference processes at quantum transitions in near- and fully-resonant optically-dense Doppler-broadened medium are studied. The feasibility of overcoming of the fundamental limitation on a…
The system of equations of self-induced transparency (SIT) for extraordinary wave in uniaxial anisotropic media by means of generalized reduction perturbation method are transformed to the coupled nonlinear Schr\"odinger equations. It is…