arXiv subjects

Vladimir I. Kruglov

Publications and source records attributed to Vladimir I. Kruglov.

26 records · Page 2Linked to original sources

arXiv2021

Chirped periodic and localized waves in a weakly nonlocal media with cubic-quintic nonlinearity

We study the propagation of one-dimentional optical beams in a weakly nonlocal medium exhibiting cubic-quintic nonlinearity. A nonlinear equation governing the evolution of the beam intensity in the nonlocal medium is derived thereby which allows us to examine whether the traveling-waves exist in such optical material. An efficient transformation is applied to obtain explicit solutions of the envelope model equation in the presence of all material parameters. We find that a variety of periodic waves accompanied with a nonlinear chirp do exist in the system in the presence of the weak nonlocality. Chirped localized intensity dips on a continuous-wave background as well as solitary waves of the bright and dark types are obtained in a long wave limit. A class of propagating chirped self-similar solitary beams is also identified in the material with the consideration of the inhomogeneities of media. The applications of the obtained self-similar structures are discussed by considering a periodic distributed amplification system.

nlin.PS↗

arXiv2019

Propagation of dipole solitons in inhomogeneous highly dispersive optical fiber media

We consider the ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schrödinger equation with varying second-, third-, and fourth-order dispersions, cubic nonlinearity, and linear gain or loss. We construct a new type of exact self-similar soliton solutions that takes the structure of dipole via a similarity transformation connected to the related constant-coefficients one. The conditions on the optical fiber parameters for the existence of these self-similar structures are also given. The results show that the contribution of all orders of dispersion is an important feature to form this kind of self-similar dipole pulse shape. The dynamic behaviors of the self-similar dipole solitons in a periodic distributed amplification system are analyzed. The significance of the obtained self-similar pulses is also discussed.

nlin.PS↗

arXiv2019

Traveling waves of nonlinear Schrödinger equation including higher order dispersions

The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schrödinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The approach is based on the reduction of the generalized nonlinear Schrödinger equation to an ordinary nonlinear differential equation. The periodic solutions obtained form one-parameter family which depend on an integration constant $p$. The solitary wave solution with ${\rm sech}^2$ shape is the limiting case of this family with $p=0$. The solutions obtained describe also a train of soliton-like pulses with ${\rm sech}^2$ shape. It is shown that the bounded solutions arise only for special domains of integration constant.

nlin.PS↗

arXiv2017

Solitary Waves in Optical Fibers Governed by Higher Order Dispersion

An exact solitary wave solution is presented for the nonlinear Schrodinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The stability of this soliton-like solution with sech2 shape is proven by the sign-definiteness of the operator and an integral of the Sobolev type. The main criteria governing the existence of such stable localized pulses propagating in optical fibers are also formulated. A unique feature of these soliton-like optical pulses propagating in a fiber with higher order dispersion is that their parameters satisfy efficient scaling relations. The main soliton solution term given by perturbation theory is also presented when absorption or gain is included in the nonlinear Schrodinger equation. We anticipate that this type of stable localized pulses could find practical applications in communications, slow-light devices and ultrafast lasers.

nlin.PS↗

arXiv2015

Lambda transition and Bose-Einstein condensation in liquid ${\rm ^4He}$

We present a theory describing the lambda transition and the Bose-Einstein condensation (BEC) in a liquid ${\rm ^4He}$ based on the diatomic quasiparticle concept. It is shown that in liquid ${\rm ^4He}$ for the temperature region $1~{\rm K}\leq{\rm T}\leq {\rm T}_λ$ the diatomic quasiparticles macroscopically populate the ground state which leads to BEC in liquid ${\rm ^4He}$. The approach yields the lambda transition temperature as ${\rm T}_λ=2.16~{\rm K}$ which is in excellent agreement with the experimental lambda temperature ${\rm T}_λ=2.17~{\rm K}$. The concept of diatomic quasiparticles also leads to superfluid and BEC fractions which are in a good agreement with the experimental data and Monte Carlo simulations.

cond-mat.other↗

arXiv2013

Model for inner structure and mass spectrum of charged leptons

We present a model where the lepton masses are the eigenvalues of relativistic nonlinear field equations. The eigenfunctions correspond in the model to lepton states with inner structure. In this picture the self-interaction leads to the bound state of electron described by the ground state solution. The variational approach based on minimization of the mass or the energy of the ground state solution is developed. The analytical solution yields the relation between the coupling constant $G_l$ of the self-interaction and the electron mass as $m_e\simeq 2.3\sqrt{\hbar c/G_l}$. This solution also leads to a finite `radius' of the electron which is about $1.9λ_e$ where $λ_e$ is the Compton length of electron.

hep-ph↗

arXiv2005

The Standard Model with Modified Asymmetric Potential

We consider a version of special relativity assuming that the metric in inertial frames is conformally pseudoeuclidean and depends on some scalar field with zero vacuum average. Applying this modified special relativity to the theory of electroweak interactions, and assuming that the introduced scalar field is proportional to the Higgs field, we show there is full consistency between the minimal Standard Model and our approach, except that, in our model, the potential in the Higgs sector is asymmetric and has two distinct vacuum states. It is found that, in the new modified model the mass of the Higgs particle is half that in the minimal Standard Model.

hep-ph↗

arXiv2003

Zero-range potentials with Inner structure: fitting parameters for resonance scattering

The solution of the classical Fermi problem of low-energy neutron scattering by nuclei, when the excitations of the nuclei in scattering processes are taken into account, is found by the method of zero-range potentials with inner structure. This model is a generalization of the Fermi zero-range potential obtained by adding a non-trivial inner Hamiltonian and inner space with indefinite metric. We propose a general principle of analyticity of the Caley-transform of the S-scattering matrix, written as a function of wave number. This permits us to evaluate all parameters of the model, including the indefinite metric tensor of the inner space, once the spectrum of the inner Hamiltonian, the scattering length and the effective radious are chosen.

quant-ph↗