arXiv subjects

M. D. Todorov

Publications and source records attributed to M. D. Todorov.

12 recordsLinked to original sources

arXiv2018

Manakov model with gain/loss terms and $N$-soliton interactions: Effects of periodic potentials

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the perturbed nonlinear Schrodinger (NLS) equation and the Manakov model. The perturbations include the simultaneous by a periodic external potential, and linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain (PCTC) models for both NLS and Manakov model. We show that the soliton interactions dynamics for the PCTC models compares favorably to full numerical results of the original perturbed NLS and Manakov model.

nlin.SI↗

arXiv2016

Adiabatic Interactions of Manakov Solitons -- Effects of Cross-modulation

We investigate the asymptotic behavior of the Manakov soliton trains perturbed by cross-modulation in the adiabatic approximation. The multisoliton interactions in the adiabatic approximation are modeled by a generalized Complex Toda chain (GCTC). The cross-modulation requires special treating for the evolution of the polarization vectors of the solitons. The numerical predictions of the Manakov system are compared with the perturbed GCTC. For certain set of initial parameters GCTC describes very well the long-time evolution of the Manakov soliton trains.

nlin.SI↗

arXiv2014

Asymptotic Behavior of Manakov Solitons: Effects of Potential Wells and Humps

We consider the asymptotic behavior of the soliton solutions of Manakov's system perturbed by external potentials. It has already been established that its multisoliton interactions in the adiabatic approximation can be modeled by the Complex Toda chain (CTC). The fact that the CTC is a completely integrable system, enables us to determine the asymptotic behavior of the multisoliton trains. In the present study we accent on the 3-soliton initial configurations perturbed by sech-like external potentials and compare the numerical predictions of the Manakov system and the perturbed CTC in different regimes. The results of conducted analysis show that the perturbed CTC can reliably predict the long-time evolution of the Manakov system.

math-ph↗

arXiv2007

Self-Compression and Controllable Guidance of Multi-Millijoule Femtosecond Laser Pulses

Self-compression of multi-millijoule femtosecond laser pulses and dramatic increase of the peak intensity are found in pressurized helium and neon within a range of intensity in which the ionization modification of the material parameters by the pulse is negligible. The pulse propagation is studied by the (3+1)-dimensional nonlinear Schroedinger equation including basic lowest order optical processes -- diffraction, group velocity dispersion of second order, and Kerr nonlinearity of third order. Smooth and well controllable pulse propagation dynamics is found. Constructing of compressed pulse of controllable parameters at given space target point can be achieved by a proper chose of the pulse energy and/or gas pressure.

physics.optics↗

arXiv2007

Self-Compression of High-Intensity Femtosecond Laser Pulses in Low Dispersion Regime

Self-compression of femtosecond laser pulses and more than an order of magnitude increase of the peak intensity is found in a positive dispersion medium in low dispersion regime based on the (3+1)-dimensional nonlinear Schr{ö}dinger equation. A method of high-intensity femtosecond pulse formation can be developed on that basis.

physics.optics↗

arXiv2000

A Free Boundary Problem in the Theory of the Stars

We investigate numerically models of the static spherically symmetric boson-fermion stars in the scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem with unknown internal boundary. To solve this problem the Continuous Analogue of Newton Method is used.

astro-ph↗

arXiv2000

Josephson Junctions with Minimal Length

The minimal length of ``one-dimensional'' Josephson junctions, in which the specific bound states of the magnetic flux retain their stability is discussed numerically. Thereby, we consider as ``long'' every Josephson junction, in which there exists at least one nontrivial stable distribution of the magnetic flux for fixed values of all the physical and the geometrical parameters. Our results can be applied for optimization of the sizes of devices containing Josephson junctions for different operating conditions.

cond-mat.supr-con↗

arXiv2000

Mathematical Modeling of Boson-Fermion Stars in the Generalized Scalar-Tensor Theories of Gravity

A model of static boson-fermion star with spherical symmetry based on the scalar-tensor theory of gravity with massive dilaton field is investigated numerically. Since the radius of star is \textit{a priori} an unknown quantity, the corresponding boundary value problem (BVP) is treated as a nonlinear spectral problem with a free internal boundary. The Continuous Analogue of Newton Method (CANM) for solving this problem is applied. Information about basic geometric functions and the functions describing the matter fields, which build the star is obtained. In a physical point of view the main result is that the structure and properties of the star in presence of massive dilaton field depend essentially both of its fermionic and bosonic components.

math.NA↗

arXiv2000

New Numerical Algorithm for Modeling of Boson-Fermion Stars in Dilatonic Gravity

We investigate numerically a models of the static spherically symmetric boson-fermion stars in scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem with unknown internal boundary. We employ the Continuous Analogue of Newton Method (CANM) which leads on each iteration to two separate linear boundary value problems with different dimensions inside and outside the star, respectively. Along with them a nonlinear algebraic system for the spectral parameters - radius of the star $R_{s}$ and quantity $Ω$ is solved also. In this way we obtain the behaviour of the basic geometric quantities and functions describing dilaton field and matter fields which build the star.

math.NA↗

arXiv1998

Finite-Difference Investigation of Axisymmetric Inviscid Separated Flows with Infinitely-Long Cusp-Ended Stagnation Zone. Flow around a Sphere

The classical Helmholtz problem is applied for modelling the axisymmetric inviscid cusp-ended separated flow around a sphere. Two coordinate systems are employed: polar for initial calculations and parabolic the latter being more suitable for investigation of infinitely-long stagnation zones. Scaled coordinates are introduced and difference schemes for the free-stream equation and the Bernoulli integral are devised. The separation point is not initially prescribed and is defined iteratively. A separated flow with vanishing drag coefficient is obtained.

physics.flu-dyn↗

arXiv1998

Numerical Investigation of a Bifurcation Problem with free Boundaries Arising from the Physics of Josephson Junctions

A direct method for calculating the minimal length of ``one-dimensional'' Josephson junctions is proposed, in which the specific distribution of the magnetic flux retains its stability. Since the length of the junctions is a variable quantity, the corresponding nonlinear spectral problem as a problem with free boundaries is interpreted. The obtained results give us warranty to consider as ``long'', every Josephson junction in which there exists at least one nontrivial stable distribution of the magnetic flux for fixed values of all other parameters.

cond-mat.supr-con↗

arXiv1998

Finite-Difference Implementation of Inviscid Separated Flows with Infinitely-Long Cusp-Ended Stagnation Zone around Circular Cylinder

The classical Helmholtz problem is applied for modelling and numerical investigation of inviscid cusp-ended separated flow around circular cylinder. Two coordinate systems are used: polar for initial calculations and parabolic as topologically most suited for infinite stagnation zone. Scaling by the shape of the unknown free line renders the problem to computational domain with fixed boundaries. Difference schemes and algorithm for Laplace equation and for Bernoulli integral are devised. A separated flow with drag coefficient $C_x=0$ like the so called ``critical'' flow is obtained. The pressure distribution on the surface of cylinder and the detachment point compares quantitatively very well with the predictions of the hodograph method.

physics.flu-dyn↗