Anastasia Doikou

Anastasia Doikou
Heriot-Watt University · Department of Mathematics

PhD

About

165
Publications
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1,699
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Publications

Publications (165)
Preprint
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We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks, called parametric (p)-shelves and racks. Generic invertible solutions of the set-theoretic reflection equation are also obtained by a suitable parametric twist. The twi...
Article
We produce novel non‐involutive solutions of the Yang–Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from braces and skew braces, and surprisingly in the case of braces, they are not necessarily involutive. In the case of two‐sided (skew) braces, one can assign such solutions to every element...
Preprint
Full-text available
The theory of the set-theoretic Yang-Baxter equation is reviewed from a purely algebraic point of view. We recall certain algebraic structures called shelves, racks and quandles. These objects satisfy a self-distributivity condition and lead to solutions of the Yang-Baxter equation. We also recall that non-involutive solutions of the braid equation...
Article
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We present connections between left non-degenerate solutions of the set-theoretic braid equation and left shelves using Drinfel’d homomorphisms. We generalize the notion of affine quandle, by using heap endomorphisms and metahomomorphisms, and identify the underlying Yang–Baxter algebra for solutions of the braid equation associated to a given quan...
Preprint
Full-text available
The theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The first step towards this objective is the introduction of certain generalizations of the familiar shelves and racks called parametric (p)-shelves and racks. These objects satisfy a parametric self-distributivity condition and lea...
Preprint
Full-text available
We present connections between left non-degenerate solutions of set-theoretic Yang-Baxter equation and left shelves using certain maps called Drinfel'd homomorphisms. We further generalise the notion of affine quandle, by using heap endomorphisms and metahomomorphisms, and identify the Yang-Baxter algebra for solutions of the braid equation associa...
Article
The workshop was focused on the interplay between set-theoretic solutions to the Yang–Baxter equation and several algebraic structures used to construct and understand new solutions. In this vein, the YBE and properties of these algebraic structures are used as a source of inspiration to study other mathematical problems not directly related to the...
Article
Motivated by recent findings on the derivation of parametric noninvolutive solutions of the Yang–Baxter equation, we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new multi‐parametric, nondegenerate, noninvolutive solutions of the set‐theoretic Yang–Baxter equation. These solutio...
Preprint
Full-text available
We present resent results regarding involutive, non-degenerate solutions of the set-theoretic Yang-Baxter and reflection equations. We recall the notion of braces and we present and prove various fundamental properties necessary for the solution of the set theoretic Yang-Baxter equation. We then consider lambda parametric set-theoretic solutions of...
Preprint
Full-text available
Motivated by recent findings on the derivation of parametric non-involutive solutions of the Yang-Baxter equation we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new multi-parametric, non-degenerate, non-involutive solutions of the set-theoretic Yang-Baxter equation. These solut...
Preprint
Full-text available
We review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a discrete version of Magnus expansion. We also systematically derive the discrete analogue of the pre-Lie Magnus expansion and show that the elements of the discrete Dyson series are expressed in terms of a tridendriform...
Article
Full-text available
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang–Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld twists, we show that the quantum algebras produced from set-theoretic solutions and their q-analogues are in fac...
Article
We examine links between the theory of braces and set-theoretical solutions of the Yang–Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras and we identify new quantum groups associated to set-theoretic solutions coming from braces. We also construct a nove...
Preprint
Full-text available
We produce novel non-involutive solutions of the Yang-Baxter equation coming from (skew) braces. These solutions are generalisations of the known ones coming from the standard braces and skew braces, and surprisingly in the case of braces they are not necessarily involutive. In the case of two-sided (skew) braces one can assign such solutions to ev...
Preprint
Full-text available
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang-Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld twists we show that the quantum algebras produced from set-theoretic solutions and their q-analogues are in fact...
Preprint
Full-text available
We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable in the sense that they are realisable as Fred-holm Grassmannian flows. In other words, time-evolutionary solutions to such systems can be constructed from solutions to the corresponding underyling linear partial differential system, by s...
Preprint
Full-text available
We demonstrate how many classes of Smoluchowski-type coagulation models can be realised as Grassmannian or nonlinear graph flows and are therefore linearisable, and/or integrable in this sense. We first prove that a general Smoluchowski-type equation with a constant frequency kernel, that encompasses a large class of such models, is realisable as a...
Article
Full-text available
We consider involutive, non-degenerate, finite set-theoretic solutions of the Yang–Baxter equation (YBE). Such solutions can be always obtained using certain algebraic structures that generalize nilpotent rings called braces. Our main aim here is to express such solutions in terms of admissible Drinfeld twists substantially extending recent prelimi...
Article
Full-text available
Connections between set-theoretic Yang–Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic R -matrices are expressed as twists of known solutions. We then focus on reflection and twisted algebras and we derive the associated defining algebra relations for R -matrices being Baxterized solutions...
Chapter
The time evolution problem for non-self-adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential equations, which naturally emerge when computing the path integral, leads to a universal expression for the asso...
Preprint
Full-text available
We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that generalize nil potent rings called braces. Our main aim here is to express such solutions in terms of admissible Drinfeld twists substantially extending recent preliminary...
Article
Full-text available
We propose the systematic construction of classical and quantum two-dimensional space-time lattices primarily based on algebraic considerations, i.e. on the existence of associated r -matrices and underlying spatial and temporal classical and quantum algebras. This is a novel construction that leads to the derivation of fully discrete integrable sy...
Article
We present a method for linearising classes of matrix-valued nonlinear partial differential equations with local and nonlocal nonlinearities. Indeed we generalise a linearisation procedure originally developed by Pöppe based on solving the corresponding underlying linear partial differential equation to generate an evolutionary Hankel operator for...
Preprint
Full-text available
We propose the systematic construction of classical and quantum two dimensional space-time lattices primarily based on algebraic considerations, i.e. on the existence of associated r-matrices and underlying spatial and temporal classical and quantum algebras. This is a novel construction that leads to the derivation of fully discrete integrable sys...
Article
Full-text available
We consider space discretizations of the matrix Zakharov–Shabat AKNS scheme, in particular the discrete matrix non-linear Scrhrödinger (DNLS) model, and the matrix generalization of the Ablowitz–Ladik (AL) model, which is the more widely acknowledged discretization. We focus on the derivation of solutions via local Darboux transforms for both discr...
Preprint
Full-text available
In this paper, we present a method for linearising certain classes of nonlinear partial differential equations. Originally constructed so as to target PDEs with nonlocal nonlinearities, herein we extend our approach in a non-commutative manner that accommodates local nonlinearities as well, thus enabling us to linearise (matrix) integrable systems....
Preprint
Full-text available
Connections between set theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We provide examples of set theoretic R-matrices expressed as simple twists of known solutions. Based on these solutions we construct the associated "twisted" co-products. Suitable generalizations regarding the q-deformed case are...
Preprint
Full-text available
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential equations, which naturally emerge when computing the path integral, leads to a universal expression for the asso...
Preprint
Full-text available
We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras and we identify new quantum groups associated to set-theoretic solutions coming from braces. We also construct a nove...
Preprint
We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras and we identify new quantum groups associated to set-theoretic solutions coming from braces. We also construct a nove...
Preprint
We consider space discretizations of the matrix Zakharov-Shabat AKNS scheme, in particular the discrete matrix non-linear Scrhrodinger (DNLS) model, and the matrix generalization of the Ablowitz-Ladik (AL) model, which is the more widely acknowledged discretization. We focus on the derivation of solutions via local Darboux transforms for both discr...
Preprint
Full-text available
We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable. By this we mean that solutions can be generated by solving a corresponding linear partial differential system together with a linear Fredholm integral equation. The flows of such nonlinear systems are examples of linear flows on Fredhol...
Preprint
Full-text available
We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable. By this we mean that solutions can be generated by solving a corresponding linear partial differential system together with a linear Fredholm integral equation. The flows of such nonlinear systems are examples of linear flows on Fredhol...
Article
Full-text available
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion of the quantum canonical transformation is employed for computing the time propagator, in the case of generic...
Article
Full-text available
We review some of the fundamental notions associated with the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and also on methods that provide solutions to partial or ordinary differential equations that are associated to discrete or continuous integrable systems. The Riccati equation...
Preprint
Full-text available
We focus on the non-linear Schrodinger model and we extend the notion of space-time dualities in the presence of integrable time-like boundary conditions. We identify the associated time-like `conserved' quantities and Lax pairs as well as the corresponding boundary conditions. In particular, we derive the generating function of the space component...
Article
Full-text available
We consider the generalized matrix non-linear Schrödinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation, and we also identify recursion relations that yield the Lax pairs for the whole matrix NLS-type hierarc...
Article
Full-text available
We focus on the non-linear Schrödinger model and we extend the notion of space-time dualities in the presence of integrable time-like boundary conditions. We identify the associated time-like “conserved” quantities and Lax pairs as well as the corresponding boundary conditions. In particular, we derive the generating function of the space component...
Preprint
We review some of the fundamental notions associated to the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and also on methods that provide solutions to partial or ordinary differential equations that display solitonic solutions and are associated to discrete or continuous integrable...
Preprint
We consider the generalized matrix non-linear Schrodinger hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation, and we also identify recursion relations that yield the Lax pairs for the whole matrix NLS hierarchy. These r...
Preprint
Full-text available
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion of the quantum canonical transformation is employed for computing the time propagator, in the case of generic...
Article
Full-text available
We develop a method for generating solutions to large classes of evolutionary partial differential systems with non-local nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow. It is analogo...
Preprint
Full-text available
We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto...
Chapter
Full-text available
We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto...
Preprint
Full-text available
We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow. It is analogou...
Data
We consider the deformed harmonic oscillator as a discrete version of the Liouville theory and study this model in the presence of local integrable defects. From this, the time evolution of the defect degrees of freedom are determined, found in the form of the local equations of motion. We also revisit the continuous Liouville theory, deriving its...
Article
Full-text available
We explore the notion of the quantum auxiliary linear problem and the associated problem of quantum Backlund transformations (BT). In this context we systematically construct the analogue of the classical formula that provides the whole hierarchy of the time components of Lax pairs at the quantum level for both closed and open integrable lattice mo...
Article
Full-text available
We show how solutions to a large class of Riccati evolutionary nonlinear partial differential equations can be generated from the corresponding linearized equations. The key is an integral equation analogous to the Marchenko equation, or more generally dressing transformation, in integrable systems. We show explicitly how this can be achieved for s...
Preprint
Full-text available
We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto...
Article
Full-text available
We consider the discrete and continuous vector non-linear Schrodinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the time part of a typical Darboux-Backlund transformation. Within this spirit we then explicitly w...
Article
Full-text available
We consider the discrete and continuous vector non-linear Schrodinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the time part of a typical Darboux-Backlund transformation. Within this spirit we then explicitly w...
Article
Full-text available
We consider the deformed harmonic oscillator as a discrete version of the Liouville theory and study this model in the presence of local integrable defects. From this, the time evolution of the defect degrees of freedom are determined, found in the form of the local equations of motion. We also revisit the continuous Liouville theory, deriving its...
Article
Full-text available
We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the equations of motion on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Backlund transformations. And although these equation...
Preprint
We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the "equations of motion" on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Backlund transformations. And although these equati...
Article
Full-text available
We study the bulk and boundary scattering of the sl(N) twisted Yangian spin chain via the solution of the Bethe ansatz equations in the thermodynamic limit. Explicit expressions for the scattering amplitudes are obtained and the factorization of the bulk scattering is shown. The issue of defects in twisted Yangians is also briefly discussed.
Article
Full-text available
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonia...
Article
Full-text available
We propose a classical analogue of the vertex algebra in the context of classical integrable field theories. We use this fundamental notion to describe the auxiliary function of the linear auxiliary problem as a classical vertex operator. Then using the underlying algebra satisfied by the auxiliary function together with the linear auxiliary proble...
Article
Full-text available
Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous presence of integrable boundaries and defects. The respective sewing conditions as well as the relevant equatio...
Article
14 pages, Latex. A few comments added. Version to appear in JSTAT
Article
Full-text available
We consider the sl(N) twisted Yangian quantum spin chain. In particular, we study the bulk and boundary scattering of the model via the solution of the Bethe ansatz equations in the thermodynamic limit. Local defects are also implemented in the model and the associated transmission amplitudes are derived through the relevant Bethe ansatz equations.
Article
Full-text available
A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of mod...
Article
Full-text available
The concept of point-like "jump" defects is investigated in the context of affine Toda field theories. The Hamiltonian formulation is employed for the analysis of the problem. The issue is also addressed when integrable boundary conditions ruled by the classical twisted Yangian are present. In both periodic and boundary cases explicit expressions o...
Data
Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous presence of integrable boundaries and defects. The respective sewing conditions as well as the relevant equatio...
Data
Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous presence of integrable boundaries and defects. The respective sewing conditions as well as the relevant equatio...
Data
Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous presence of integrable boundaries and defects. The respective sewing conditions as well as the relevant equatio...
Article
Full-text available
Classical integrable impurities associated to high rank (gl_N) algebras are investigated. A particular prototype i.e. the vector non-linear Schr\"{o}dinger (NLS) model is chosen as an example. A systematic construction of local integrals of motion as well as the time components of the corresponding Lax pairs is presented based on the underlying cla...
Article
Full-text available
Type-I quantum defects are considered in the context of the gl_N spin chain. The type-I defects are associated to the generalized harmonic oscillator algebra, and the chosen defect matrix is the one of the vector non-linear Schrodinger (NLS) model. The transmission matrices relevant to this particular type of defects are computed via the Bethe ansa...
Article
The and quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices — representations of the underlying quadratic algebra — that physically describe the interaction between the various particle-lik...
Article
Full-text available
Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical...
Article
Full-text available
The \( \mathfrak{g}{{\mathfrak{l}}_{\mathcal{N}}} \) and \( {{\mathfrak{U}}_q}\left( {\mathfrak{g}{{\mathfrak{l}}_{\mathcal{N}}}} \right) \) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matri...
Article
Full-text available
The sine-Gordon model in the presence of dynamical integrable defects is investigated. This is an application of the algebraic formulation introduced for integrable defects in earlier works. The quantities in involution as well as the associated Lax pairs are explicitly extracted. Integrability i also shown using certain sewing constraints, which e...
Article
Full-text available
We consider the Heisenberg spin chain in the presence of integrable spin defects. Using the Bethe ansatz methodology, we extract the associated transmission amplitudes, that describe the interaction between the particle-like excitations displayed by the models and the spin impurity. In the attractive regime of the XXZ model, we also derive the brea...
Article
Full-text available
Point-like Liouville integrable dynamical defects are introduced in the context of the Landau-Lifshitz and Principal Chiral (Faddeev-Reshetikhin) models. Based primarily on the underlying quadratic algebra we identify the first local integrals of motion, the associated Lax pairs as well as the relevant sewing conditions around the defect point. The...
Article
Full-text available
Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the ent...
Article
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Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete and continuum classical integrable models is introduced. Using this framework the associated classical integr...
Article
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In this paper, solutions of the generic non-compact Weyl equation are obtained. In particular, by identifying a suitable similarity transformation and introducing a non-trivial change of variables we are able to implement azimuthal dependence on the solutions of the diagonal non-compact Weyl equation. We also discuss some open questions related to...
Article
Full-text available
A systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrodinger model in the presence of a single particle-like defect is investigated through this algebraic approach. Local integrals of motions are constructed as well as the time components of the corresponding Lax p...
Article
Full-text available
We construct SU(n + 1) Bogomolny-Prasad-Sommerfeld (BPS) spherically symmetric monopoles with minimal symmetry breaking by solving the full Weyl equation. In this context, we explore and discuss the existence of open spin chainlike part within the Weyl equation. For instance, in the SU(3) case the relevant spin chain is the 2-site spin 1/2XXX chain...
Article
We apply the ADHMN construction to obtain the SU(n+1) (for generic values of n) spherically symmetric BPS monopoles with minimal symmetry breaking. In particular, the problem simplifies by solving the Weyl equation, leading to a set of coupled equations, whose solutions are expressed in terms of the Whittaker functions. Next, this construction is g...
Article
Full-text available
The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to set...
Article
Full-text available
We study the classical generalized gl(n) Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary Hamiltonian for the sl(2) L-L model. Novel expressions of the modified Lax pairs associated to the integrals of moti...
Article
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A non-compact version of the Weyl equation is proposed, based on the infinite dimensional spin zero representation of the \mathfraks\mathfrakl2 \mathfrak{s}{\mathfrak{l}_2} algebra. Solutions of the aforementioned equation are obtained in terms of the Kummer functions. In this context, we discuss the ADHMN approach in order to construct the corre...
Article
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We present certain classical continuum long wave-length limits of prototype integrable quantum spin chains, and define the corresponding construction of classical continuum Lax operators. We also provide two specific examples, i.e. the isotropic and anisotropic Heisenberg models.
Article
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In this paper, we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang–Baxter and boundary Yang–Baxter equations depending on the choice of boundary conditions. The relation between the aforementioned equation...
Article
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A general framework for obtaining certain types of contracted and centrally extended algebras is reviewed. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
Article
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We apply the ADHMN construction to obtain the SU(n+1)(for generic values of n) spherically symmetric BPS monopoles with minimal symmetry breaking. In particular, the problem simplifies by solving the Weyl equation, leading to a set of coupled equations, whose solutions are expressed in terms of the Whittaker functions. Next, this construction is ge...
Article
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We examine certain classical continuum long wave-length limits of prototype integrable quantum spin chains. We define the corresponding construction of classical continuum Lax operators. Our discussion starts with the XXX chain, the anisotropic Heisenberg model and their generalizations and extends to the generic isotropic and anisotropic gln magne...

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