Papers by Michail Todorov
ABSTRACT The spatiotemporal dynamics of high‐intensity femtosecond laser pulses is studied within... more ABSTRACT The spatiotemporal dynamics of high‐intensity femtosecond laser pulses is studied within a rigorous physical model. The pulse propagation is described by the nonlinear envelope equation. The propagation and the material equations are solved self‐consistently at realistic physical conditions. Self‐compression of the pulse around single‐cycle regime and dramatic increase of the pulse intensity is found. At certain conditions, the peak intensity, transversal width, time duration, and the spatiotemporal pulse shape remain stable with the propagation of the pulse, resembling a soliton formation process. This, to our knowledge, is the first simulation of high‐intensity ultrashort soliton formation dynamics in the (3+1)‐dimensional case.
AIP Conference Proceedings, 2007
The no-scalar-hair theorems do not apply in the case when non-linear electrodynamics is included ... more The no-scalar-hair theorems do not apply in the case when non-linear electrodynamics is included in the theory. In the current work, some preliminary numerical results describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massive scalar field are presented.
Modern Physics Letters A, 2008
Recent results show that when nonlinear electrodynamics is considered, the no-scalar-hair theorem... more Recent results show that when nonlinear electrodynamics is considered, the no-scalar-hair theorems in the scalar–tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented.1,2 What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to nonlinear electrodynamics in a special class of scalar–tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar–tensor theories considered, the black holes have a single, non-degenerate horizon, i.e. their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of...
Modern Physics Letters A, 2007
The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a s... more The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a scalar dressing for a large class of theories. No-scalar-hair theorems have been proved for the cases of neutral black holes and for charged black holes in the Maxwell electrodynamics. These theorems, however, do not apply in the case of nonlinear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Euler–Heisenberg type nonlinear electrodynamics in scalar–tensor theories of gravity with massless scalar field are found. In comparison to the corresponding solution in General Relativity the presented solution has a simpler causal structure the reason for which is the presence of the scalar field. The present class of black holes has a single, nondegenerate horizon, i.e. its causal structure resembles that of the Schwarzschild black hole.
The European Physical Journal Plus, 2021
Nonlinear waves have long been at the research focus of both physicists and mathematicians, in di... more Nonlinear waves have long been at the research focus of both physicists and mathematicians, in diverse settings ranging from electromagnetic waves in nonlinear optics to matter waves in Bose-Einstein condensates, from Langmuir waves in plasma to internal and rogue waves in hydrodynamics. The study of physical phenomena by means of mathematical models often leads to nonlinear evolution equations known as integrable systems. One of the distinguished features of integrable systems is that they admit soliton solutions, i.e., stable, localized traveling waves which preserve their shape and velocity in the interaction. Other fundamental properties of integrable systems are their universal nature, and the fact that they can be effectively linearized, e.g., via the Inverse Scattering Transform (IST), or reduced to appropriate Riemann-Hilbert problems. Moreover, explicit solutions can often be derived by the Zakharov-Shabat dressing method, by Bäcklund or Darboux transformations, or by Hirota's bilinear method. Prototypical examples of such integrable equations in 1+1 dimensions are the nonlinear Schrödinger (NLS) equation and its multicomponent generalizations, the sine-Gordon equation, the Korteweg-de Vries (KdV) and the modified KdV equations, the Kulish-Sklyanin model, etc. The most notable examples of integrable systems in 2+1-dimensions are the Kadomtsev-Petviashvili (KP) equations, and the Davey-Stewartson equations. The aim of this special issue is to present the latest developments in the theory of nonlinear waves and integrable systems, and some of their applications. Below, we briefly outline the contributions to the present Focus Point (FP) summarizing their achievements in nonlinear wave phenomena and integrable systems. Some open problems and questions are also identified.
Nucleation and Atmospheric Aerosols, 2017
We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the no... more We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.
Nucleation and Atmospheric Aerosols, 2013
We derive the perturbed complex Toda chain (PCTC) as a model describing the adiabatic interaction... more We derive the perturbed complex Toda chain (PCTC) as a model describing the adiabatic interactions of N Manakov solitons with sech-like external potentials. We demonstrate that such potentials can cause transitions between the different asymptotic regimes of the solitons. The predictions of PCTC and the Manakov model are compared numerically and shown to match very well.
arXiv (Cornell University), Jul 21, 2020
We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the Ma... more We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the Manakov model. The evolution of Manakov N-soliton trains is described by the complex Toda chain (CTC) which is a completely integrable dynamical model. Calculating the eigenvalues of its Lax matrix allows us to determine the asymptotic velocity of each soliton. So we describe sets of soliton parameters that ensure one of the two main types of asymptotic regimes: the bound state regime (BSR) and the free asymptotic regime (FAR). In particular we find explicit description of special symmetric configurations of N solitons that ensure BSR and FAR. We find excellent matches between the trajectories of the solitons predicted by CTC with the ones calculated numerically from the Manakov system for wide classes of soliton parameters. This confirms the validity of our model.
arXiv (Cornell University), Jan 15, 2018
We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the pe... more We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the perturbed nonlinear Schrödinger equation (NLSE) 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 NLSE and Manakov model.
Nucleation and Atmospheric Aerosols, 2015
High-intensity ultrashort laser pulse propagation in bulk nonlinear medium is studied in ionizati... more High-intensity ultrashort laser pulse propagation in bulk nonlinear medium is studied in ionization-free regime. The propagation properties of the pulse is described within (3+1)-dimensional cubic-quintic nonlinear envelope equation. A smooth pulse propagation dynamics free of abrupt changes of the pulse parameters is observed. A robust compressed pulse is predicted for the first time in ionization-free regime at realistic physical conditions.
Springer eBooks, 2014
The spatiotemporal dynamics of high-intensity femtosecond laser pulses is studied in strongly non... more The spatiotemporal dynamics of high-intensity femtosecond laser pulses is studied in strongly nonlinear regime. The physical model is capable to describe ultrashort pulse propagation down to single-cycle regime at presence of ionization of the medium. The ionization contribution to the group velocity dispersion is introduced in the model. The pulse propagation is described by the nonlinear envelope equation. The propagation and material equations are solved self-consistently at realistic physical conditions. We have shown that, at typical laboratory scale distances, the linear processes, more particularly – the dispersion, play a secondary role, while the pulse propagation dynamics is ruled mainly by competitive nonlinear processes in neutrals and plasma.
Journal of Physics B, Aug 3, 2007
Self-compression of femtosecond laser pulses and more than an order of magnitude increase of the ... more 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 Schrödinger equation. A method of high-intensity femtosecond pulse formation can be developed on that basis.
Optics Communications, Jul 1, 2014
Abstract The spatiotemporal dynamics of high-intensity femtosecond laser pulses is studied within... more Abstract The spatiotemporal dynamics of high-intensity femtosecond laser pulses is studied within a rigorous physical model. The pulse propagation is described by the nonlinear envelope equation. The propagation and the material equations are solved self-consistently at realistic physical conditions. Self-compression of the pulse is found. At certain conditions, transversal width, peak intensity, time duration, and spatiotemporal shape of the pulse remain stable within given propagation range.
Nonlinear systems and complexity, Oct 21, 2013
We analyze the dynamical behavior of the N-soliton train in adiabatic approximation of the Manako... more We analyze the dynamical behavior of the N-soliton train in adiabatic approximation of the Manakov system (MS) perturbed by three types of external potentials: periodic, quadratic and quartic ones. We show that the dynamics of the N-soliton train is modeled by a perturbed complex Toda chain for certain choices of the train parameters and for small magnitudes of the intensities of the potentials. Possible applications of these results for Bose-Einstein condensates are discussed.
Nonlinear Systems and Complexity, 2013
We analyze the dynamical behavior of the N-soliton train in adiabatic approximation of the Manako... more We analyze the dynamical behavior of the N-soliton train in adiabatic approximation of the Manakov system (MS) perturbed by three types of external potentials: periodic, quadratic and quartic ones. We show that the dynamics of the N-soliton train is modeled by a perturbed complex Toda chain for certain choices of the train parameters and for small magnitudes of the intensities of the potentials. Possible applications of these results for Bose-Einstein condensates are discussed.
AIP Conference Proceedings, 2015
We demonstrate that properly varying the polarization vectors one can substantially influence the... more We demonstrate that properly varying the polarization vectors one can substantially influence the soliton interactions. In particular, one can make three soliton bound state to go into mixed asymptotic regime or into free asymptotic regime.
We derive the perturbed complex Toda chain (PCTC) as a model describing the adiabatic interaction... more We derive the perturbed complex Toda chain (PCTC) as a model describing the adiabatic interactions of N Manakov solitons with sech-like external potentials. We demonstrate that such potentials can cause transitions between the different asymptotic regimes of the solitons. The predictions of PCTC and the Manakov model are compared numerically and shown to match very well.
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Papers by Michail Todorov