arXiv subjects

S. B. Leble

Publications and source records attributed to S. B. Leble.

9 recordsLinked to original sources

arXiv2006

Mode interaction in multi-mode optical fibers with Kerr effect

We generalize the projection to orthogonal function basis (including polarization modes) method for nonlinear (Kerr medium) fiber and use this method in a case of two-mode waveguide. We consider orthogonal Bessel functions basis that fit the choice of cylindrical geometry of a fiber. The coupled nonlinear Schrödinger equations (CNLS) are derived. Analytic expressions and numerical results for coupling coefficients are given; the fiber parameters dependence is illustrated by plots.

physics.optics↗

arXiv2006

Piecewise continuous distribution function method and ultrasound at half space

The system of hydrodynamic-type equations, derived by two-side distribution function for a stratified gas in gravity field is applied to a problem of ultrasound propagation and attenuation. The background state and linearized version of the obtained system is studied and compared with the Navier-Stokes one at arbitrary Knudsen numbers. The WKB solutions for ultrasound in a stratified medium are constructed in explicit form. The problem of a generation by a moving plane in a rarefied gas is explored and used as a test while compared with experiment.

physics.ao-ph↗

arXiv2005

Polarization mode interaction equations in optical fibers with Kerr effect

We derive coupled nonlinear Schrödinger equation (CNLSE) for arbitrary polarized light propagation in a single-mode fiber. We introduce a basis of transverse eigen modes with the appropriate projecting hence solutions depend on the waveguide geometry. Considering a weak nonlinearity which is connected with Kerr effect, we give explicit expressions for nonlinear constants via integrals of Bessel functions. We compare numerical results for the nonlinear constant extracted from experimental observations of a soliton for the nonlinear Schrödinger equation (NLSE) (single-mode one). The method of projecting we use allows a direct generalization to multi-mode fiber case.

physics.optics↗

arXiv2004

Piecewise continuous partition function method in the theory of wave perturbations of inhomogeneous gas

The problem of wave disturbance propagation in rarefied gas in gravity field is explored. The system of hydrodynamic-type equations for a stratified gas in gravity field is derived from BGK equation by method of piecewise continuous partition function. The obtained system of the equations generalizes the Navier-Stokes at arbitrary density (Knudsen numbers). The verification of the model is made for a limiting case of a homogeneous medium. Results are in the good agreement with experiment and former theories at arbitrary Knudsen numbers.

physics.flu-dyn↗

arXiv2002

Numerical integration of coupled Korteweg-de Vries System

We introduce a numerical method for general coupled Korteweg-de Vries systems. The scheme is valid for solving Cauchy problems for arbitrary number of equations with arbitrary constant coefficients. The numerical scheme takes its legality by proving its stability and convergence which gives the conditions and the appropriate choice of the grid sizes. The method is applied to Hirota-Satsuma (HS) system and compared with its known explicit solution investigating the influence of initial conditions and grid sizes on accuracy. We also illustrate the method to show the effects of constants with a transition to non-integrable cases.

math.NA↗

arXiv2002

Analytical and numerical solution of a coupled KdV-MKdV system

The matrix 2x2 spectral differential equation of the second order is considered on x in ($-\infty,+\infty$). We establish elementary Darboux transformations covariance of the problem and analyze its combinations. We select a second covariant equation to form Lax pair of a coupled KdV-MKdV system. The sequence of the elementary Darboux transformations of the zero-potential seed produce two-parameter solution for the coupled KdV-MKdV system with reductions. We show effects of parameters on the resulting solutions (reality, singularity). A numerical method for general coupled KdV-MKdV system is introduced. The method is based on a difference scheme for Cauchy problems for arbitrary number of equations with constants coefficients. We analyze stability and prove the convergence of the scheme which is also tested by numerical simulation of the explicit solutions.

math-ph↗

arXiv2002

A dressing of zero-range potentials and electron-molecule scattering problem at low energies

A dressing of a nonspherical potential, which includes $n$ zero range potentials, is considered. The dressing technique is used to improve ZRP model. Concepts of the partial waves and partial phases for non-spherical potential are used in order to perform Darboux transformation. The problem of scattering on the regular $\hbox{X}_n$ and $\hbox{YX}_n$ structures is studied. The possibilities of dressed ZRP are illustrated by model calculation of the low-energy electron-Silane ($\hbox{SiH}_4$) scattering. The results are discussed. Key words: multiple scattering, silane, zero range potential.

quant-ph↗

arXiv2000

Darboux-integration of idρ/dt=[H,f(ρ)]

A Darboux-type method of solving the nonlinear von Neumann equation $i\dot ρ=[H,f(ρ)]$, with functions $f(ρ)$ commuting with $ρ$, is developed. The technique is based on a representation of the nonlinear equation by a compatibility condition for an overdetermined linear system. von Neumann equations with various nonlinearities $f(ρ)$ are found to possess the so-called self-scattering solutions. To illustrate the result we consider the Hamiltonian $H$ of a one-dimensional harmonic oscillator and $f(ρ)=ρ^q-2ρ^{q-1}$ with arbitary real $q$. It is shown that self-scattering solutions possess the same asymptotics for all $q$ and that different nonlinearities may lead to effectively indistinguishable evolutions. The result may have implications for nonextensive statistics and experimental tests of linearity of quantum mechanics.

quant-ph↗

arXiv1998

On exact solutions of Maxwell-Bloch system for two-level medium with degeneracy

Maxwell-Bloch system describing the resonant propagation of electromagnetic pulses in both two-level media with degeneracy in angle moment projection and three-level media with equal oscillator forces is considered. The inhomogeneous broadening of energy levels is accounted. Binary Darboux Transformation generating the solutions of the system is constructed. Pulses corresponding to the transition between levels with largest population difference are shown to be stable. The solution describing the propargation of pulses in the medium exited by the periodic wave is obtained. The hierarchy of infinitesimal symmetries is obtained by means of Darboux transformation.

quant-ph↗