arXiv subjects

G. T. Adamashvili

Publications and source records attributed to G. T. Adamashvili.

At least 19 recordsLinked to original sources

arXiv2026

Nonlinear waves: a review Vector $0π$ pulse and the generalized perturbative reduction 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 reduced to vector (coupled) nonlinear Schrodinger equations for auxiliary functions. This approach demonstrates that, unlike McCall and Hahn SIT theory in which single-component scalar breather can propagate independently, in the more general theory of SIT the second derivatives with respect to the spatial coordinate and time of the wave equation play a significant role and describe the interaction of two scalar SIT breathers forming a coupled pair. This is a vector 0πpulse of SIT - a two-component vector breather oscillating with the sum and difference of frequencies and wave numbers. The profile, parameters and properties of this pulse differ significantly from the characteristics of the McCall and Hahn pulses. Using GPRM it is shown that besides the scalar soliton and the scalar breather, the vector $0π$ pulse is also a universal nonlinear wave, arising in virtually all areas of physics where nonlinear phenomena are described by nonlinear equations containing second-order and higher-order derivatives. A number of such nonlinear equations are presented. Among them almost all well known nonlinear equations, as well as the general fourth-order nonlinear partial differential equation and the sixth-order generalized Boussinesq-type equations.

cond-mat.mes-hall↗

arXiv2025

Two-component nonlinear wave solutions of the sixth-order generalised Boussinesq-type equations

Two different versions of cubic sixth-order generalised Boussinesq-type wave equations are considered in this study. A generalised perturbation reduction method is used to solve these equations, which allows the reduction of considered equations to coupled nonlinear Schrodinger equations. Two-component nonlinear wave solutions are obtained. The profiles and parameters of these solutions for both nonlinear equations are presented and compared. These solutions coincide with the vector 0 πpulse of self-induced transparency, which was previously studied in several known nonlinear wave equations.

nlin.SI↗

arXiv2024

Two-component nonlinear waves

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 waves in the different areas of physics. Using both the slowly varying envelope approximation and the generalized perturbation reduction method, the generalized equation is transformed into the coupled nonlinear Schrodinger equations and the two-component nonlinear solitary wave solution is obtained. Explicit analytical expressions for the shape and parameters of two-component nonlinear wave consisting of two breathers oscillating with the sum and difference frequencies and wave numbers are presented. The solution of the generalized equation coincides with the vector 0πpulse of the self-induced transparency.

nlin.PS↗

arXiv2023

Two-component breather solution of the nonlinear wave equation

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 varying envelope approximation and the generalized perturbative reduction method, the nonlinear wave equation was transformed to coupled nonlinear Schrodinger equations for auxiliary functions. An explicit analytical solution of a nonlinear wave equation in the form of a two-breather molecule was obtained. One breather oscillated with the sum, and the other with the difference of frequencies and wave numbers. The obtained solution coincides with the solutions of the two-breather molecule found in a number of well-known equations from different areas of physics. It is shown that in a particular case of the small amplitude waves, a solution in the form of a two-breather molecule for the nonlinear Klein-Gordon equation coincides with the vector 0πpulse of the self-induced transparency which is presented under less stringent conditions compared to the same solution of this equation obtained earlier.

nlin.PS↗

arXiv2023

Two-component nonlinear wave of the cubic Boussinesq-type equation

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. Using the slowly varying envelope approximation and the generalized perturbation reduction method the cubic Boussinesq-type equation is transformed to the coupled nonlinear Schrodinger equations and the two-component nonlinear solitary wave solution is obtained. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse oscillating with the sum and difference of the frequencies and wave numbers are presented. It is shown that obtained solution coincides with the vector $0π$ pulse of the self-induced transparency.

nlin.PS↗

arXiv2021

Two-component breather solution of the nonlinear Klein-Gordon equation

The generalized perturbative reduction method is used to find the two-component vector breather solution of the nonlinear Klein-Gordon equation. It is shown that the nonlinear pulse oscillates with the sum and difference of frequencies and wave numbers in the region of the carrier wave frequency and wave number. Explicit analytical expressions for the profile and parameters of the nonlinear pulse are obtained. In the particular case, the vector breather coincides with the vector $0π$ pulse of self-induced transparency.

nlin.PS↗

arXiv2021

Two-component nonlinear wave of the Born-Infeld equation

The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - σU_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown that the solution of the two-component nonlinear wave oscillates with the sum and difference of frequencies and wave numbers.

nlin.PS↗

arXiv2021

Two-component nonlinear wave of the cubic Boussinesq equation

In this work, we employ the generalized perturbation reduction method to find the two-component vector breather solution of the cubic Boussinesq equation $U_{tt} - C U_{zz} - D U_{zzzz}+G (U^{3})_{zz}=0$. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse oscillating with the sum and difference of the frequencies and wave numbers are obtained.

cond-mat.mes-hall↗

arXiv2021

Two-component nonlinear wave of the Hirota equation

Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schrödinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The components of the pulse oscillate with the sum and difference of the frequencies and the wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.

cond-mat.mes-hall↗

arXiv2020

Two-component nonlinear wave of the NLS equation

Using the generalized perturbation reduction method the scalar nonlinear Schrödinger equation is transformed to the coupled nonlinear Schrödinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The components of the pulse oscillate with the sum and difference of the frequencies and wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.

nlin.SI↗

arXiv2020

Two-component vector breather solution of the modified BBM equation

This is a continuation of Ref.[1](arXiv:nlin.PS/2001.07758v1). In the present paper, we consider the solution to the modified Benjamin-Bona-Mahony equation $u_{ t} + C u_{z} + βu_{zzt} + a u^{2} u_{z}=0$ using the generalized perturbation reduction method. The equation is transformed to the coupled nonlinear Schrödinger equations for auxiliary functions. Explicit analytical expression for the shape and parameters of the two-component vector breather oscillating with the sum and difference of frequencies and wavenumbers are obtained.

nlin.SI↗

arXiv2020

Light-Matter Interaction and Hybrid Vector Breather

The nonlinear coherent interaction of light with the dispersive and Kerr-type third-order susceptibility medium containing optical impurity atoms or semiconductor quantum dots is considered. Using the generalized perturbation reduction method, the nonlinear wave equation is reduced to the coupled nonlinear Schrödinger equations. It is shown that the second-order derivatives play a key role in the description of the process of formation of the bound state of two breathers oscillating with the sum and the difference of frequencies and wave numbers. The resonant, nonresonant and hybrid mechanisms of the formation of the two-component nonlinear pulse -- the vector breather are realized depending on the light and medium parameters. Explicit analytical expressions for the profile and parameters of the nonlinear pulse are presented. The conditions of the excitation of resonant, nonresonant and hybrid nonlinear waves are discussed. In the particular case, the resonant vector breather coincides with the vector $0π$ pulse of self-induced transparency.

nlin.PS↗

arXiv2020

Breather solutions of the modified Benjamin-Bona-Mahony equation

New two-component vector breather solution of the modified Benjamin-Bona-Mahony (MBBM) equation is considered. Using the generalized perturbation reduction method the MBBM equation is reduced to the coupled nonlinear Schrödinger equations for auxiliary functions. Explicit analytical expressions for the profile and parameters of the vector breather oscillating with the sum and difference of the frequencies and wavenumbers are presented. The two-component vector breather and single-component scalar breather of the MBBM equation is compared.

nlin.PS↗

arXiv2019

Vector $0π$ pulse in anisotropic media

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 Schrödinger equations. It is shown that in the theory of SIT the second derivatives have significant role and leads to the formation of a vector $0π$ pulse oscillating with the sum and difference of the frequencies. An explicit analytical expressions for the profile and parameters of the nonlinear wave are obtained. It is shown that along with scalar $2π$ pulse, the vector $0π$ pulse is also the basic pulse of SIT and the scalar $0π$ pulse of SIT is only an approximation which can be considered in some special cases. The conditions of the existence of the nonlinear extraordinary wave depends on the direction of propagation. The profile of the vector $0π$ pulse in anisotropic crystal of ruby is presented with characteristic parameters which usually met in experiments.

cond-mat.mes-hall↗

arXiv2018

Vector pulsing solitons in Kerr media

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 nonresonance vector pulsing soliton with the difference and sum of the frequencies is presented. Explicit analytical expressions for the optical two-component vector pulsing soliton with phase modulation are obtained. It is shown that the two-component pulsing soliton in this special case can be transformed to the scalar pulsing soliton,and these waves have different profiles.

nlin.PS↗

arXiv2017

Optical two-photon nonlinear waves in two-dimensional materials

A theory of an optical two-photon breather in a graphene monolayer (or graphene-like two-dimensional material) is constructed. The system of the material equations for two-photon transitions and the wave equation for transverse magnetic polarized modes of the surface plasmon polaritons are shown to reduce to the nonlinear Schrödinger equation with damping. Explicit analytical expressions for a surface small intensity two-photon breather (0$π$ pulse) of self-induced transparency are obtained. It is shown that the optical conductivity of graphene reduces the amplitude of the surface two-photon nonlinear wave during the propagation. The one-photon and two-photon breathers in graphene are compared and have obtained that the differences between their parameters are significant.

cond-mat.mes-hall↗

arXiv2014

Vector Pulsing Solitons in Semiconductor Quantum Dots

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 dots and phase modulation changes significantly the pulse parameters. The profile of a circularly polarized optical two-component vector pulsing soliton with the difference and sum of the frequencies in the region of the carrier frequency is presented. It is shown that the vector pulsing soliton in the special case can be reduced to the scalar breather solution and these nonlinear waves have different shapes. Explicit analytical expressions for the optical vector pulsing soliton are obtained with realistic parameters which can be reached in current experiments.

cond-mat.mes-hall↗

arXiv2010

Beer's law in semiconductor quantum dots

The propagation of a coherent optical linear wave in an ensemble of semiconductor quantum dots is considered. It is shown that a distribution of transition dipole moments of the quantum dots changes significantly the polarization and Beer's absorption length of the ensemble of quantum dots. Explicit analytical expressions for these quantities are presented.

physics.optics↗