Georgi Georgiev Grahovski
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Georgi Georgiev Grahovski has a total of 44 co-authors. Here are the top co-authors by number of shared publications:
- Vladimir Stefanov Gerdjikov
Institute of Mathematics and Informatics Bulgarian Academy of Sciences Sofia Bulgaria
12 shared publications - Rossen I. Ivanov
School of Mathematics and Statistics Technological University Dublin Dublin Ireland
6 shared publications Vladimir S. Gerdjikov
Varna Free University “Chernorizec Hrabar”, Chayka Resort, Varna, 9007, Bulgaria
5 shared publications- Alexander V. Mikhailov
Department of Applied Mathematics University of Leeds Leeds UK
4 shared publications Vladimir Gerdjikov
4 shared publicationsMarissa Condon
School of Electronic Engineering Dublin City University Glasnevin, Dublin 9, Ireland
3 shared publications
Latest Publications
- 13 April 2024
- Published by World Scientific Pub Co Pte Ltd in International Journal of Geometric Methods in Modern Physics
- Vol. 21 (10)
On the N-waves hierarchy with constant boundary conditions. Spectral properties
This paper is devoted to [ ]-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators [ ], whose potentials [ ] tend to constants [ ] for [ ]. For special choices of [ ], we outline the spectral properties of [ ], the direct scattering transform and construct its fundamental analytic solutions. We generalize Wronskian relations for the case of CBC — this allows us to analyze the mapping between the scattering data and the [ ]-derivative of the potential [ ]. Next, using the Wronskian relations, we derive the dispersion laws for the [ ]-wave hierarchy and describe the NLEE related to the given Lax operator.
- 13 April 2024
- Published by World Scientific Pub Co Pte Ltd in International Journal of Geometric Methods in Modern Physics
- Vol. 21 (10)
On the N-waves hierarchy with constant boundary conditions. Spectral properties
This paper is devoted to [ ]-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators [ ], whose potentials [ ] tend to constants [ ] for [ ]. For special choices of [ ], we outline the spectral properties of [ ], the direct scattering transform and construct its fundamental analytic solutions. We generalize Wronskian relations for the case of CBC — this allows us to analyze the mapping between the scattering data and the [ ]-derivative of the potential [ ]. Next, using the Wronskian relations, we derive the dispersion laws for the [ ]-wave hierarchy and describe the NLEE related to the given Lax operator.
- Open Access
- 28 March 2024
- Published by Springer Nature in The European Physical Journal B
- Vol. 97 (3) , 1-8
Thermodynamic properties of disordered quantum spin ladders
In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( $$r=0$$ ) case up to the diluted ( $$r \rightarrow 1$$ ) limit, and for selected choices of number of legs $$L_y$$ per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $$L_y$$ . Graphical- 28 March 2024
- Published by Springer Nature in The European Physical Journal B
- Vol. 97 (3) , 1-8
Open AccessThermodynamic properties of disordered quantum spin ladders
In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( $$r=0$$ ) case up to the diluted ( $$r \rightarrow 1$$ ) limit, and for selected choices of number of legs $$L_y$$ per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $$L_y$$ . Graphical - Open Access
On the $N$-waves hierarchy with constant boundary conditions. Spectral properties
The paper is devoted to $N$-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators $L$, whose potentials $Q(x,t)$ tend to constants $Q_\pm$ for $x\to \pm \infty$. For special choices of $Q_\pm$ we outline the spectral properties of $L$, the direct scattering transform and construct its fundamental analytic solutions. We generalise Wronskian relations for the case of CBC -- this allows us to analyse the mapping between the scattering data and the $x$-derivative of the potential $Q_x$. Next, using the Wronskian relations we derive the dispersion laws for the $N$-wave hierarchy and describe the NLEE related to the given Lax operator.Open AccessOn the $N$-waves hierarchy with constant boundary conditions. Spectral properties
The paper is devoted to $N$-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators $L$, whose potentials $Q(x,t)$ tend to constants $Q_\pm$ for $x\to \pm \infty$. For special choices of $Q_\pm$ we outline the spectral properties of $L$, the direct scattering transform and construct its fundamental analytic solutions. We generalise Wronskian relations for the case of CBC -- this allows us to analyse the mapping between the scattering data and the $x$-derivative of the potential $Q_x$. Next, using the Wronskian relations we derive the dispersion laws for the $N$-wave hierarchy and describe the NLEE related to the given Lax operator. - Open Access
Thermodynamic properties of disordered quantum spin ladders
In this paper, we study the thermodynamic properties of spin-$1/2$ antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths $r$, from the clean ($r=0$) case up to the diluted ($r \rightarrow 1$) limit, and for selected choices of number of legs $L_y$ per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in $r$, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $L_y$.Open AccessThermodynamic properties of disordered quantum spin ladders
In this paper, we study the thermodynamic properties of spin-$1/2$ antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths $r$, from the clean ($r=0$) case up to the diluted ($r \rightarrow 1$) limit, and for selected choices of number of legs $L_y$ per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in $r$, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $L_y$. - Open AccessOn affine Toda field theories related to ${\bf D}_r$ algebras and their real Hamiltonian formsThe paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series ${\bf D}_r$. We demonstrate that the complexification procedure followed by a restriction to a specified real Hamiltonian form commutes with the external automorphisms of $\mathfrak{g}$. This is illustrated on the examples ${\bf D}_{r+1}^{(1)} \to {\bf B}_r^{(1)}$ and ${\bf D}_4^{(1)} \to {\bf G}_2^{(1)}$ using external automorphisms of the corresponding extended Dynkin diagrams.Open AccessOn affine Toda field theories related to ${\bf D}_r$ algebras and their real Hamiltonian formsThe paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series ${\bf D}_r$. We demonstrate that the complexification procedure followed by a restriction to a specified real Hamiltonian form commutes with the external automorphisms of $\mathfrak{g}$. This is illustrated on the examples ${\bf D}_{r+1}^{(1)} \to {\bf B}_r^{(1)}$ and ${\bf D}_4^{(1)} \to {\bf G}_2^{(1)}$ using external automorphisms of the corresponding extended Dynkin diagrams.
- 26 August 2022
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 212 (2) , 1053-1072
Real Hamiltonian forms of affine Toda field theories: Spectral aspects
The paper is devoted to real Hamiltonian forms of \(2\)-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of “reductions ” of Hamiltonian systems, similar to real forms of semisimple Lie algebras. Examples of real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac–Moody algebras are studied. Along with the associated Lax representations, we also formulate the relevant Riemann–Hilbert problems and derive the minimal sets of scattering data that uniquely determine the scattering matrices and the potentials of the Lax operators.- 26 August 2022
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 212 (2) , 1053-1072
Real Hamiltonian forms of affine Toda field theories: Spectral aspects
The paper is devoted to real Hamiltonian forms of \(2\)-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of “reductions ” of Hamiltonian systems, similar to real forms of semisimple Lie algebras. Examples of real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac–Moody algebras are studied. Along with the associated Lax representations, we also formulate the relevant Riemann–Hilbert problems and derive the minimal sets of scattering data that uniquely determine the scattering matrices and the potentials of the Lax operators.- 1 October 2018
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 197 (1) , 1430-1450
Nonlocal Reductions of The Multicomponent Nonlinear Schrödinger Equation on Symmetric Spaces
Our aim is to develop the inverse scattering transform for multicomponent generalizations of nonlocal reductions of the nonlinear Schrödinger (NLS) equation with [equation]symmetry related to...
- 1 October 2018
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 197 (1) , 1430-1450
Nonlocal Reductions of The Multicomponent Nonlinear Schrödinger Equation on Symmetric Spaces
Our aim is to develop the inverse scattering transform for multicomponent generalizations of nonlocal reductions of the nonlinear Schrödinger (NLS) equation with [equation]symmetry related to...
- 1 October 2018
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 197 (1) , 1412-1429
Nonlocal Reductions of the Ablowitz–Ladik Equation
Our purpose is to develop the inverse scattering transform for the nonlocal semidiscrete nonlinear Schrödinger equation (called the Ablowitz–Ladik equation) with [equation]symmetry. This includes...
- 1 October 2018
- Published by Pleiades Publishing Ltd in Theoretical and Mathematical Physics
- Vol. 197 (1) , 1412-1429
Nonlocal Reductions of the Ablowitz–Ladik Equation
Our purpose is to develop the inverse scattering transform for the nonlocal semidiscrete nonlinear Schrödinger equation (called the Ablowitz–Ladik equation) with [equation]symmetry. This includes...
- Open Access
On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
The aim of this paper is to develop the inverse scattering transform (IST) for multi-component generalisations of nonlocal reductions of the nonlinear Schrodinger (NLS) equation with PT-symmetry related to symmetric spaces. This includes: the spectral properties of the associated Lax operator, Jost function, the scattering matrix and the minimal set of scattering data, the fundamental analytic solutions. As main examples, we use the Manakov vector Schr\"odinger equation (related to A.III-symmetric spaces) and the multi-component NLS (MNLS) equations of Kullish-Sklyanin type (related to BD.I-symmetric spaces). Furthermore, the 1- and 2-soliton solutions are obtained by using an appropriate modification of the Zakharov-Shabat dressing method. It is shown, that the MNLS equations of these types allow both regular and singular soliton configurations. Finally, we present here different examples of 1- and 2-soliton solutions for both types of models, subject to different reductions.
Open AccessOn nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
The aim of this paper is to develop the inverse scattering transform (IST) for multi-component generalisations of nonlocal reductions of the nonlinear Schrodinger (NLS) equation with PT-symmetry related to symmetric spaces. This includes: the spectral properties of the associated Lax operator, Jost function, the scattering matrix and the minimal set of scattering data, the fundamental analytic solutions. As main examples, we use the Manakov vector Schr\"odinger equation (related to A.III-symmetric spaces) and the multi-component NLS (MNLS) equations of Kullish-Sklyanin type (related to BD.I-symmetric spaces). Furthermore, the 1- and 2-soliton solutions are obtained by using an appropriate modification of the Zakharov-Shabat dressing method. It is shown, that the MNLS equations of these types allow both regular and singular soliton configurations. Finally, we present here different examples of 1- and 2-soliton solutions for both types of models, subject to different reductions.
- Open Access
Nonlocal reductions of the Ablowitz-Ladik equation
The purpose of the present paper is to develop the inverse scattering transform for the nonlocal semi-discrete nonlinear Schrodinger equation (known as Ablowitz-Ladik equation) with PT-symmetry. This includes: the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data and the fundamental analytic solutions. In addition, the paper studies the spectral properties of the associated discrete Lax operator. Based on the formulated (additive) Riemann-Hilbert problem, the 1- and 2-soliton solutions for the nonlocal Ablowitz-Ladik equation are derived. Finally, the completeness relation for the associated Jost solutions is proved. Based on this, the expansion formula over the complete set of Jost solutions is derived. This will allow one to interpret the inverse scattering transform as a generalised Fourier transform.
Open AccessNonlocal reductions of the Ablowitz-Ladik equation
The purpose of the present paper is to develop the inverse scattering transform for the nonlocal semi-discrete nonlinear Schrodinger equation (known as Ablowitz-Ladik equation) with PT-symmetry. This includes: the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data and the fundamental analytic solutions. In addition, the paper studies the spectral properties of the associated discrete Lax operator. Based on the formulated (additive) Riemann-Hilbert problem, the 1- and 2-soliton solutions for the nonlocal Ablowitz-Ladik equation are derived. Finally, the completeness relation for the associated Jost solutions is proved. Based on this, the expansion formula over the complete set of Jost solutions is derived. This will allow one to interpret the inverse scattering transform as a generalised Fourier transform.