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Papers by Assen Kyuldjiev

Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), Nov 1, 2015

The effects of the external potential wells on the Manakov soliton interactions using the perturb... more The effects of the external potential wells on the Manakov soliton interactions using the perturbed complex Toda chain (PCTC) model are analyzed. The superposition of a large number of wells/humps influences stronger the motion of the soliton envelopes and can cause a transition from asymptotically free and mixed asymptotic regime to a bound state regime and vice versa. Such external potentials are easier to implement in experiments and can be used to control the soliton motion in a given direction and to achieve a predicted motion of the optical pulse. A general feature of the conducted numerical experiments is that the long-time evolution of both CTC and PCTC match very well with the Manakov model numerics, often much longer than expected even for 9-soliton train configurations. This means that PCTC is reliable dynamical model for predicting the evolution of the multisoliton solutions of Manakov model in adiabatic approximation.

Physical review, Dec 15, 1982

Several possible ionization mechanisms of excited F centers (F*) in alkali halides are discussed.... more Several possible ionization mechanisms of excited F centers (F*) in alkali halides are discussed. A lattice tunneling model for the low-temperature F* ionization is proposed which implies considerable rearrangement of the lattice as a condition for a radiationless electron transfer from the F* center to a virtual polaron center in the crystal. This model rests on a configurational diagram based on experimental absorption and emission data. A recent reaction-rate theory of electron hopping in polar crystals is applied to calculate the rate constant k &2 of the F~i onization in the temperature range 10-160 K by the use of reasonable values of four parameters: the LO vibration frequency v, the reorganization energy E"ofthe lattice, the reaction heat Q at zero temperature, and the resonance energy V&2 of the electron transfer. In this way good agreement between the theoretical results and the available experimental data for k&2 is obtained. In addition, an independent estimation of the "average" resonance energy, based on a simple donor-acceptor model for the electron transfer, is found to agree very well with the values of Vl2 fitted to the experiment. The average values of the electron tunneling distanceE, and the average donor-acceptor (F-centerpolaron-center) separation R derived from this model seem also to be quite reasonable. Some implications of the theory concerning the reverse process of electron transfer from a free polaron to an empty ion vacancy are also discussed.

Proceedings of the Estonian Academy of Sciences, 2015

The soliton interactions of Manakov soliton trains subjected to composite external potentials are... more The soliton interactions of Manakov soliton trains subjected to composite external potentials are modelled by the perturbed complex Toda chain (PCTC). The model is applied to several classes of potentials, such as: (i) harmonic, (ii) periodic, (iii) 'wide well'-type potentials, and (iv) inter-channel interactions. We demonstrate that the potentials can change the asymptotic regimes of the soliton trains. Our results can be implemented, e.g., in experiments on Bose-Einstein condensates and can be used to control the soliton motion. In general, our numerical experiments demonstrate that the predictions of complex Toda chain (CTC) (respectively PCTC) match very well the Manakov (respectively perturbed Manakov) model numerics for long-time evolution, often much longer than expected. This means that both CTC and PCTC are reliable dynamical models for predicting the dynamics of the multisoliton trains of the Manakov model in adiabatic approximation. This extends our previous results on scalar soliton trains to the Manakov trains with compatible initial parameters.

Mathematics and Computers in Simulation, 2016

We consider the asymptotic behavior of the soliton solutions of Manakov's system perturbed by ext... more 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.

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.

AIP Conference Proceedings, 2014

Wave Motion, 2017

We investigate the asymptotic behavior of the Manakov soliton trains perturbed by cross-modulatio... more 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.

arXiv (Cornell University), Oct 18, 2022

The European Commission's support for the production of this publication does not constitute an e... more The European Commission's support for the production of this publication does not constitute an endorsement of the contents, which reflect the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

arXiv (Cornell University), Dec 18, 2022

The European Commission's support for the production of this publication does not constitute an e... more The European Commission's support for the production of this publication does not constitute an endorsement of the contents, which reflect the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

Wave Motion, 2011

Several important examples of the N-wave equations are studied. These integrable equations can be... more Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann-Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic Nwave equations but mainly the 3-and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with Z2 × Z2 reduction group allows breather-like solitons. Finally it is demonstrated that RHP with sewing function depending on three variables t, x and y provides some special solutions of the N-wave equations in three dimensions.

Letters in Mathematical Physics, 1985

Nonlocal hidden symmetry transformations with a generalized structure and boundary conditions at ... more Nonlocal hidden symmetry transformations with a generalized structure and boundary conditions at spatial infinity for the principal chiral model are proposed. Additional restrictions on these transformations following from the requirement for the existence of an infinite set of conserved nonlocal charges are analyzed. The corresponding Lie algebra is more general than the Kac-Moody one.

The European Physical Journal B - Condensed Matter, 2002

ABSTRACT We consider generalizations of the standard Hamiltonian dynamics to complex dynamical va... more ABSTRACT We consider generalizations of the standard Hamiltonian dynamics to complex dynamical variables and introduce the notions of real Hamiltonian form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real Hamiltonian system we are able to relate several nonequivalent ones. On the example of the complex Toda chain we demonstrate how starting from a known integrable Hamiltonian system (e.g. the Toda chain) one can complexify it and then project onto different real forms.

European Journal of Nuclear Medicine, 1985

The European Physical Journal B, 2004

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the noti... more We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate another nonequivalent (real) ones. A crucial role in this construction is played by the assumed analyticity and the invariance of the Hamiltonian under the involution. We show that if the initial system is Liouville integrable, then its complexification and its real forms will be integrable again and this provides a method of finding new integrable systems starting from known ones. We demonstrate our construction by finding real forms of dynamics for the Toda chain and a family of Calogero-Moser models. For these models we also show that the involution of the complexified phase space induces a Cartan-like involution of their Lax representations.

The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortun... more The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortunately, it does not come from a coordinate change in the configuration space of the initial model and actually defines a new dynamical system. So, it is a questionable approach to the problem but it is shown here that the final result could still make sense as a Marsden-Weinstein reduced system. (This reduction can be seen as completely analogous to the procedure of obtaining the “centrifugal ” potential in the classical Kepler problem.) It is shown that in the standard linearization approximation of the Coulomb gauged Higgs model geometrical constraint theory offers an explanation of the Higgs mechanism because solving of the Gauss law constraint leads to different physical submanifolds which are not preserved by the action of the (broken) global U(1) group.

arXiv: General Physics, 1999

The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortun... more The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortunately, it does not come from a coordinate change in the configuration space of the initial model and actually defines a new dynamical system. So, it is a questionable approach to the problem but it is shown here that the final result could still make sense as a Marsden-Weinstein reduced system. (This reduction can be seen as completely analogous to the procedure of obtaining the "centrifugal" potential in the classical Kepler problem.) It is shown that in the standard linearization approximation of the Coulomb gauged Higgs model geometrical constraint theory offers an explanation of the Higgs mechanism because solving of the Gauss law constraint leads to different physical submanifolds which are not preserved by the action of the (broken) global U(1) group.

Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), Nov 1, 2015

The effects of the external potential wells on the Manakov soliton interactions using the perturb... more The effects of the external potential wells on the Manakov soliton interactions using the perturbed complex Toda chain (PCTC) model are analyzed. The superposition of a large number of wells/humps influences stronger the motion of the soliton envelopes and can cause a transition from asymptotically free and mixed asymptotic regime to a bound state regime and vice versa. Such external potentials are easier to implement in experiments and can be used to control the soliton motion in a given direction and to achieve a predicted motion of the optical pulse. A general feature of the conducted numerical experiments is that the long-time evolution of both CTC and PCTC match very well with the Manakov model numerics, often much longer than expected even for 9-soliton train configurations. This means that PCTC is reliable dynamical model for predicting the evolution of the multisoliton solutions of Manakov model in adiabatic approximation.

Physical review, Dec 15, 1982

Several possible ionization mechanisms of excited F centers (F*) in alkali halides are discussed.... more Several possible ionization mechanisms of excited F centers (F*) in alkali halides are discussed. A lattice tunneling model for the low-temperature F* ionization is proposed which implies considerable rearrangement of the lattice as a condition for a radiationless electron transfer from the F* center to a virtual polaron center in the crystal. This model rests on a configurational diagram based on experimental absorption and emission data. A recent reaction-rate theory of electron hopping in polar crystals is applied to calculate the rate constant k &2 of the F~i onization in the temperature range 10-160 K by the use of reasonable values of four parameters: the LO vibration frequency v, the reorganization energy E"ofthe lattice, the reaction heat Q at zero temperature, and the resonance energy V&2 of the electron transfer. In this way good agreement between the theoretical results and the available experimental data for k&2 is obtained. In addition, an independent estimation of the "average" resonance energy, based on a simple donor-acceptor model for the electron transfer, is found to agree very well with the values of Vl2 fitted to the experiment. The average values of the electron tunneling distanceE, and the average donor-acceptor (F-centerpolaron-center) separation R derived from this model seem also to be quite reasonable. Some implications of the theory concerning the reverse process of electron transfer from a free polaron to an empty ion vacancy are also discussed.

Proceedings of the Estonian Academy of Sciences, 2015

The soliton interactions of Manakov soliton trains subjected to composite external potentials are... more The soliton interactions of Manakov soliton trains subjected to composite external potentials are modelled by the perturbed complex Toda chain (PCTC). The model is applied to several classes of potentials, such as: (i) harmonic, (ii) periodic, (iii) 'wide well'-type potentials, and (iv) inter-channel interactions. We demonstrate that the potentials can change the asymptotic regimes of the soliton trains. Our results can be implemented, e.g., in experiments on Bose-Einstein condensates and can be used to control the soliton motion. In general, our numerical experiments demonstrate that the predictions of complex Toda chain (CTC) (respectively PCTC) match very well the Manakov (respectively perturbed Manakov) model numerics for long-time evolution, often much longer than expected. This means that both CTC and PCTC are reliable dynamical models for predicting the dynamics of the multisoliton trains of the Manakov model in adiabatic approximation. This extends our previous results on scalar soliton trains to the Manakov trains with compatible initial parameters.

Mathematics and Computers in Simulation, 2016

We consider the asymptotic behavior of the soliton solutions of Manakov's system perturbed by ext... more 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.

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.

AIP Conference Proceedings, 2014

Wave Motion, 2017

We investigate the asymptotic behavior of the Manakov soliton trains perturbed by cross-modulatio... more 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.

arXiv (Cornell University), Oct 18, 2022

The European Commission's support for the production of this publication does not constitute an e... more The European Commission's support for the production of this publication does not constitute an endorsement of the contents, which reflect the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

arXiv (Cornell University), Dec 18, 2022

The European Commission's support for the production of this publication does not constitute an e... more The European Commission's support for the production of this publication does not constitute an endorsement of the contents, which reflect the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

Wave Motion, 2011

Several important examples of the N-wave equations are studied. These integrable equations can be... more Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann-Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic Nwave equations but mainly the 3-and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with Z2 × Z2 reduction group allows breather-like solitons. Finally it is demonstrated that RHP with sewing function depending on three variables t, x and y provides some special solutions of the N-wave equations in three dimensions.

Letters in Mathematical Physics, 1985

Nonlocal hidden symmetry transformations with a generalized structure and boundary conditions at ... more Nonlocal hidden symmetry transformations with a generalized structure and boundary conditions at spatial infinity for the principal chiral model are proposed. Additional restrictions on these transformations following from the requirement for the existence of an infinite set of conserved nonlocal charges are analyzed. The corresponding Lie algebra is more general than the Kac-Moody one.

The European Physical Journal B - Condensed Matter, 2002

ABSTRACT We consider generalizations of the standard Hamiltonian dynamics to complex dynamical va... more ABSTRACT We consider generalizations of the standard Hamiltonian dynamics to complex dynamical variables and introduce the notions of real Hamiltonian form in analogy with the notion of real forms for a simple Lie algebra. Thus to each real Hamiltonian system we are able to relate several nonequivalent ones. On the example of the complex Toda chain we demonstrate how starting from a known integrable Hamiltonian system (e.g. the Toda chain) one can complexify it and then project onto different real forms.

European Journal of Nuclear Medicine, 1985

The European Physical Journal B, 2004

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the noti... more We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate another nonequivalent (real) ones. A crucial role in this construction is played by the assumed analyticity and the invariance of the Hamiltonian under the involution. We show that if the initial system is Liouville integrable, then its complexification and its real forms will be integrable again and this provides a method of finding new integrable systems starting from known ones. We demonstrate our construction by finding real forms of dynamics for the Toda chain and a family of Calogero-Moser models. For these models we also show that the involution of the complexified phase space induces a Cartan-like involution of their Lax representations.

The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortun... more The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortunately, it does not come from a coordinate change in the configuration space of the initial model and actually defines a new dynamical system. So, it is a questionable approach to the problem but it is shown here that the final result could still make sense as a Marsden-Weinstein reduced system. (This reduction can be seen as completely analogous to the procedure of obtaining the “centrifugal ” potential in the classical Kepler problem.) It is shown that in the standard linearization approximation of the Coulomb gauged Higgs model geometrical constraint theory offers an explanation of the Higgs mechanism because solving of the Gauss law constraint leads to different physical submanifolds which are not preserved by the action of the (broken) global U(1) group.

arXiv: General Physics, 1999

The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortun... more The standard approach to Higgs mechanism is based on the existence of unitary gauge but, unfortunately, it does not come from a coordinate change in the configuration space of the initial model and actually defines a new dynamical system. So, it is a questionable approach to the problem but it is shown here that the final result could still make sense as a Marsden-Weinstein reduced system. (This reduction can be seen as completely analogous to the procedure of obtaining the "centrifugal" potential in the classical Kepler problem.) It is shown that in the standard linearization approximation of the Coulomb gauged Higgs model geometrical constraint theory offers an explanation of the Higgs mechanism because solving of the Gauss law constraint leads to different physical submanifolds which are not preserved by the action of the (broken) global U(1) group.