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Journal articles on the topic 'Integrable model'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ning, Wang. "Integrable Bogoliubov Transform and Integrable Model." Chinese Physics Letters 20, no. 2 (2003): 177–79. http://dx.doi.org/10.1088/0256-307x/20/2/301.

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2

Bardakçi, Korkut, Luis M. Bernardo, and Nir Sochen. "Integrable generalized Thirring model." Nuclear Physics B 487, no. 1-2 (1997): 513–25. http://dx.doi.org/10.1016/s0550-3213(96)00715-8.

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3

Karnaukhov, Igor N. "Integrable multiparametric impurity model." Physical Review B 50, no. 20 (1994): 15385–88. http://dx.doi.org/10.1103/physrevb.50.15385.

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4

Nucci, M. C., and P. G. L. Leach. "An integrable SIS model." Journal of Mathematical Analysis and Applications 290, no. 2 (2004): 506–18. http://dx.doi.org/10.1016/j.jmaa.2003.10.044.

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5

Franceschini, Chiara, Rouven Frassek, and Cristian Giardinà. "Integrable heat conduction model." Journal of Mathematical Physics 64, no. 4 (2023): 043304. http://dx.doi.org/10.1063/5.0138013.

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We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis–Marchioro–Presutti (KMP) model, the finite chain is coupled at its ends with two reservoirs that break the conservation of energy when working at different temperatures. At variance with KMP, the model considered here is integrable, and one can write in a closed form the n-point correlation functions of the non-equilibrium steady state. As a consequence of the exact solution one, can directly prove tha

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6

Guo, Xiurong, Yufeng Zhang, and Xuping Zhang. "Two Expanding Integrable Models of the Geng-Cao Hierarchy." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/860935.

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As far as linear integrable couplings are concerned, one has obtained some rich and interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling) reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. Another one is an expanding integrable model which is different from the first one. Finally, the Hamiltonian structures

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7

Nikolov, Svetoslav G., and Vassil M. Vassilev. "Integrability in a Nonlinear Model of Swing Oscillatory Motion." Journal of Geometry and Symmetry in Physics 65 (March 30, 2023): 93–108. http://dx.doi.org/10.7546/jgsp-65-2023-93-108.

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Nonlinear dynamical systems can be studied in many different directions: i)~finding integrable cases and their analytical solutions, ii)~investigating the algebraic nature of the integrability, iii)~topological analysis of integrable systems, and so on. The aim of the present paper is to find integrable cases of a dynamical system describing the rider and the swing pumped (from the seated position) as a compound pendulum. As a result of our analytical calculations, we can conclude that this system has two integrable cases when: 1)~the dumbbell lengths and point-masses meet a special condition;

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8

Yu-Feng, Zhang. "A generalized SHGI integrable hierarchy and its expanding integrable model." Chinese Physics 13, no. 3 (2004): 307–11. http://dx.doi.org/10.1088/1009-1963/13/3/008.

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9

Fokicheva, V. V., and A. T. Fomenko. "Integrable billiards model important integrable cases of rigid body dynamics." Doklady Mathematics 92, no. 3 (2015): 682–84. http://dx.doi.org/10.1134/s1064562415060095.

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10

Yan, Zhao-Wen. "On the Heisenberg Supermagnet Model in (2+1)-Dimensions." Zeitschrift für Naturforschung A 72, no. 4 (2017): 331–37. http://dx.doi.org/10.1515/zna-2016-0397.

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AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

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11

Gao, Bian, Jifeng Cui, Xiaoli Wang, and Zhaowen Yan. "(2 + 1)-Dimensional generalized third-order Heisenberg supermagnet model." International Journal of Geometric Methods in Modern Physics 15, no. 11 (2018): 1850185. http://dx.doi.org/10.1142/s0219887818501852.

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The Heisenberg supermagnet model is an important supersymmetric integrable system which is the super extension of the Heisenberg ferromagnet model. By virtue of introducing the general auxiliary matrix variables, we construct a new [Formula: see text]-dimensional generalized integrable Heisenberg supermagnet models under two constraints. Meanwhile, we establish their corresponding gauge equivalent counterparts. Moreover, we derive new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

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12

KLINKHAMER, F. R. "AN INTEGRABLE XY-MODEL REVISITED." International Journal of Modern Physics A 04, no. 20 (1989): 5453–57. http://dx.doi.org/10.1142/s0217751x89002338.

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An exactly solvable two-dimensional model of Fateev and Zamolodchikov is shown to approach, in a certain limit, the standard XY-model at zero temperature. This model may be of some relevance to strings (and to knot theory perhaps).

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13

Schlottmann, P. "Integrable Two-Impurity Kondo Model." Physical Review Letters 80, no. 22 (1998): 4975–78. http://dx.doi.org/10.1103/physrevlett.80.4975.

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14

Lechtenfeld, Olaf, Liuba Mazzanti, Silvia Penati, Alexander D. Popov, and Laura Tamassia. "Integrable noncommutative sine-Gordon model." Nuclear Physics B 705, no. 3 (2005): 477–503. http://dx.doi.org/10.1016/j.nuclphysb.2004.10.050.

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15

Bevilacqua, J. S., and W. Sessin. "An Integrable Model for Helene." Symposium - International Astronomical Union 152 (1992): 227–30. http://dx.doi.org/10.1017/s0074180900091191.

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The goal of our work is to determine the influence of Enceladus in the motion of Helene. We constructed a model considering an oblated central body (Saturn) and three satellites (Enceladus, Dione and Helene) under the action of central forces. The development of the potential was made assuming small eccentricities, null inclinations and two resonances present in this system (2:1 between Enceladus and Dione and 1:1 between Dione and Helene). The mean Hamiltonian preserves terms derived of the oblateness of the central body and also terms of both resonant arguments. The auxiliary Hori's system g

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16

Yang, Fan, Yu-peng Wang, Shu Chen, and Fu-ke Pu Fu-Cho Pu. "An Integrable Bose Fermion Model." Chinese Physics Letters 16, no. 11 (1999): 787–89. http://dx.doi.org/10.1088/0256-307x/16/11/003.

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17

Zhang, Yufeng, and Xiurong Guo. "A (2+1)-dimensional integrable hierarchy and its extending integrable model." Chaos, Solitons & Fractals 27, no. 2 (2006): 555–59. http://dx.doi.org/10.1016/j.chaos.2005.03.050.

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18

GHOSH, SASANKA. "HIGHER SPIN SYMMETRY AND SU(2) WZNW MODEL." Modern Physics Letters A 09, no. 26 (1994): 2389–98. http://dx.doi.org/10.1142/s0217732394002264.

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Generators of an infinite number of conserved charges of the integrable SU(2) WZNW model are identified with the generators of a W1+∞ symmetry algebra. This integrable conformal field theory also describes the ZN symmetric Ising model at the critical point in the large-N limit.

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19

LI, ZHU, and HUANHE DONG. "NEW INTEGRABLE LATTICE HIERARCHY AND ITS INTEGRABLE COUPLING." International Journal of Modern Physics B 23, no. 23 (2009): 4791–800. http://dx.doi.org/10.1142/s0217979209053114.

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New hierarchy of Liouville integrable lattice equation and their Hamiltonian structure are generated by use of the Tu model. Then, integrable couplings of the obtained system is worked out by the extending spectral problem.

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20

Guo, Xiu-Rong, Fang-Fang Ma, and Juan Wang. "On (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy." Thermal Science 25, no. 6 Part B (2021): 4431–39. http://dx.doi.org/10.2298/tsci2106431g.

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This paper mainly investigates the reductions of an integrable coupling of the Levi hierarchy and an expanding model of the (2+1)-dimensional Davey-Stewartson hierarchy. It is shown that the integrable coupling system of the Levi hierarchy possesses a quasi-Hamiltonian structure under certain constraints. Based on the Lie algebras construct, The type abstraction hierarchy scheme is used to gener?ate the (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy.

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21

GE, XIANG-YU. "INTEGRABLE BOUNDARY CONDITIONS FOR THE q-DEFORMED EXTENDED HUBBARD MODEL." Modern Physics Letters B 13, no. 15 (1999): 499–507. http://dx.doi.org/10.1142/s0217984999000634.

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Integrable open-boundary condition for the q-deformed Essler–Korepin–Schoutens extended Hubbard model of strongly correlated electrons are studied in the framework of the boundary quantum inverse scattering method. Diagonal boundary K-matrices are found and nine classes of integrable boundary terms are determined.

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22

Jiang, Yunfeng. "TT¯ Deformation: A Lattice Approach." Symmetry 15, no. 12 (2023): 2212. http://dx.doi.org/10.3390/sym15122212.

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Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theories on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between a sine-Gordon model and a six-vertex model on a light-cone lattice. We propose an integrable deformation of the light-cone lattice model such that in the continuum limit we obtain the TT¯-deformed sine-Gordon model. Under this deformation, the cut-off momentum becomes energy dependent and the underlying Yang–Baxter integrability is preserved. Therefore, this def

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23

Myrzakul, Akbota, and Ratbay Myrzakulov. "Integrable motion of two interacting curves, spin systems and the Manakov system." International Journal of Geometric Methods in Modern Physics 14, no. 07 (2017): 1750115. http://dx.doi.org/10.1142/s0219887817501158.

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Integrable spin systems are an important subclass of integrable (soliton) nonlinear equations. They play important role in physics and mathematics. At present, many integrable spin systems were found and studied. They are related with the motion of three-dimensional curves. In this paper, we consider a model of two moving interacting curves. Next, we find its integrable reduction related with some integrable coupled spin system. Then, we show that this integrable coupled spin system is equivalent to the famous Manakov system.

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24

Feng, Binlu, Yufeng Zhang, and Huanhe Dong. "A Few Integrable Couplings of Some Integrable Systems and (2+1)-Dimensional Integrable Hierarchies." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/932672.

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Two high-dimensional Lie algebras are presented for which four (1+1)-dimensional expanding integrable couplings of the D-AKNS hierarchy are obtained by using the Tu scheme; one of them is a united integrable coupling model of the D-AKNS hierarchy and the AKNS hierarchy. Then (2+1)-dimensional DS hierarchy is derived by using the TAH scheme; in particular, the integrable couplings of the DS hierarchy are obtained.

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25

Arnaudon, D., R. Poghossian, A. Sedrakyan, and P. Sorba. "Integrable chain model with additional staggered model parameter." Nuclear Physics B 588, no. 3 (2000): 638–55. http://dx.doi.org/10.1016/s0550-3213(00)00409-0.

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26

Yuan, Wei, and Yufeng Zhang. "A multi-component integrable hierarchy and its multi-component expanding integrable model." Chaos, Solitons & Fractals 31, no. 3 (2007): 611–16. http://dx.doi.org/10.1016/j.chaos.2005.10.038.

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27

JURČO, BRANISLAV. "LARGE-N AND BETHE ANSATZ." Modern Physics Letters A 19, no. 22 (2004): 1661–67. http://dx.doi.org/10.1142/s0217732304014859.

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We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brézin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal polynomials and saddle point approximation. Large-N limit of the matrix model corresponds to the thermodynamic limit of the integrable system. In this limit (functional) Bethe ansatz is the same as the generating function for correlators of the matrix models.

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28

S. Hemalatha and K. Annadurai. "INVENTORY MODEL INVOLVING LEAD TIME CRASHING COST AS AN EXPONENTIAL FUNCTION WITH ORDERING COST REDUCTION DEPENDENT ON LEAD TIME." jnanabha 54, no. 02 (2024): 306–14. https://doi.org/10.58250/jnanabha.2024.54231.

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We prove the existence of maximal and minimal integrable solutions of nonlinear Urysohn type integral equations. Two basic integral inequalities are obtained in the form of extremal integrable solutions which are further exploited for proving the boundedness and uniqueness of the integrable solutions of the considered integral equation.

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29

Cao, Yusong, and Junpeng Cao. "Exact Solution of a Non-Hermitian Generalized Rabi Model." Chinese Physics Letters 38, no. 8 (2021): 080202. http://dx.doi.org/10.1088/0256-307x/38/8/080202.

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An integrable non-Hermitian generalized Rabi model is constructed. A twist matrix is introduced to the construction of Hamiltonian and generates the non-Hermitian properties. The Yang-Baxter integrability of the system is proven. The exact energy spectrum and eigenstates are obtained using the Bethe ansatz. The method given in this study provides a general way to construct integrable spin-boson models.

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30

Öz, Yahya, and Andreas Klümper. "A Hubbard model with integrable impurity." Journal of Physics A: Mathematical and Theoretical 52, no. 32 (2019): 325001. http://dx.doi.org/10.1088/1751-8121/ab2cf4.

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31

Vilasi, G. "An integrable model in general relativity." European Physical Journal B - Condensed Matter 29, no. 2 (2002): 207–10. http://dx.doi.org/10.1140/epjb/e2002-00287-5.

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32

Bariev, R. Z. "Integrable model of interacting XY chains." Journal of Physics A: Mathematical and General 24, no. 16 (1991): L919—L923. http://dx.doi.org/10.1088/0305-4470/24/16/007.

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33

Sergeev, S. M. "Solitons in a 3d integrable model." Physics Letters A 265, no. 5-6 (2000): 364–68. http://dx.doi.org/10.1016/s0375-9601(99)00849-x.

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34

Cirilo-Lombardo, D. J., and V. D. Gershun. "Integrable hydrodynamic chains for WZNW Model." Physics of Particles and Nuclei Letters 11, no. 7 (2014): 1009–15. http://dx.doi.org/10.1134/s1547477114070140.

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35

Giglio, Francesco, Giulio Landolfi, and Antonio Moro. "Integrable extended van der Waals model." Physica D: Nonlinear Phenomena 333 (October 2016): 293–300. http://dx.doi.org/10.1016/j.physd.2016.02.010.

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36

Korokin, D., and H. Nicolai. "An integrable model of quantum gravity." Physics Letters B 356, no. 2-3 (1995): 211–16. http://dx.doi.org/10.1016/0370-2693(95)00832-6.

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37

Zotov, A. V., and A. M. Levin. "Integrable Model of Interacting Elliptic Tops." Theoretical and Mathematical Physics 146, no. 1 (2006): 45–52. http://dx.doi.org/10.1007/s11232-006-0005-9.

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38

Mikhailov, A. V., and A. B. Shabat. "Integrable deformations of the Heisenberg model." Physics Letters A 116, no. 4 (1986): 191–94. http://dx.doi.org/10.1016/0375-9601(86)90313-0.

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39

Oh, Phillial. "Integrable extension of nonlinear sigma model." Journal of Physics A: Mathematical and General 31, no. 17 (1998): L325—L330. http://dx.doi.org/10.1088/0305-4470/31/17/004.

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40

Zhao-Wen, Yan, Li Min-Li, Wu Ke, and Zhao Wei-Zhong. "Integrable Deformations of Heisenberg Supermagnetic Model." Communications in Theoretical Physics 53, no. 1 (2010): 21–24. http://dx.doi.org/10.1088/0253-6102/53/1/05.

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41

Rylands, Colin, Bruno Bertini, and Pasquale Calabrese. "Integrable quenches in the Hubbard model." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 10 (2022): 103103. http://dx.doi.org/10.1088/1742-5468/ac98be.

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Abstract We study the quench dynamics of the one-dimensional Hubbard model through the quench action formalism. We introduce a class of integrable initial states—expressed as product states over two sites—for which we can provide an exact characterisation of the late-time regime. This is achieved by finding a closed-form expression for the overlaps between our states and the Bethe ansatz eigenstates, which we check explicitly in the limits of low densities and infinite repulsion. Our solution gives access to the stationary values attained by local observables (we show the explicit example of t

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42

Kupershmidt, B. A. "An algebraic model of graded calculus of variations." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (1987): 151–66. http://dx.doi.org/10.1017/s0305004100066494.

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The modern theory of integrable systems rests on two fundamental pillars: the classification of Lax [13] and zero-curvature equations [14, 1, 2]; and algebraic models of the classical calculus of variations [9,5] specialized to the residue calculus in modules of differential forms over rings of matrix pseudo-differential operators [9, 6]. Both these aspects of the theory are by now very well understood for integrable systems in one space dimension.

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43

Vakhnenko, Oleksiy O. "Davydov–Kyslukha model as the starting point in the development of integrable multi-component nonlinear dynamical systems on quasi-one-dimensional lattices." Low Temperature Physics 48, no. 11 (2022): 962–69. http://dx.doi.org/10.1063/10.0014597.

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The Davydov–Kyslukha nonlinear exciton-phonon model on a regular one-dimensional lattice is asserted to be the driving force for the development of integrable multi-component nonlinear dynamical systems encompassing excitonic, vibrational and orientational degrees of freedom. The two most representative quasi-one-dimensional integrable multi-component nonlinear systems inspired by the Davydov–Kyslukha model are presented explicitly in their concise Hamiltonian forms. The new six-subsystem integrable nonlinear model on a regular quasi-one-dimensional lattice is proposed and its derivation based

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44

BRACKEN, PAUL. "AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY." International Journal of Modern Physics A 20, no. 07 (2005): 1503–14. http://dx.doi.org/10.1142/s0217751x0502104x.

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The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is show

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45

Smirnov, Aleksandr O., and Eugeni A. Frolov. "On the Propagation Model of Two-Component Nonlinear Optical Waves." Axioms 12, no. 10 (2023): 983. http://dx.doi.org/10.3390/axioms12100983.

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Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. In this paper, we propose a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. To construct the hierarchical equations, we use the monodromy matrix method, as first proposed by B.A. Dubrovin. The method we use consists of solving the following sequence of problems. First, using the Lax operator, we find th

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46

Cattaneo, Alberto S., Pavel Mnev, and Nicolai Reshetikhin. "Poisson Sigma Model and Semiclassical Quantization of Integrable Systems." Reviews in Mathematical Physics 30, no. 06 (2018): 1840004. http://dx.doi.org/10.1142/s0129055x18400044.

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In this paper, we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the target space being the phase space of the integrable system. The semiclassical path integral is defined as a formal power series with coefficients being Feynman diagrams. We also argue that in a similar way one can obtain irreducible semiclassical representations of Kontsevich’s star product. Dedicated to the memory of L. D. Faddeev

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47

Henry, BI. "Integrability of Low Particle-number Models for Solids." Australian Journal of Physics 44, no. 1 (1991): 1. http://dx.doi.org/10.1071/ph910001.

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We introduce a model Hamiltonian that describes, for different choices of the parameters, simple anharmonic models for a solid. We have applied the Painleve test to identify integrable and non-integrable cases. In the integrable cases the identification has been confirmed by deriving explicit expressions for the additional conserved quantities. The analysis demonstrates the sensitivity of lattice integrability to both the order of the anharmonicity and the nature of the boundary conditions.

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48

DOIKOU, ANASTASIA. "SELECTED TOPICS IN CLASSICAL INTEGRABILITY." International Journal of Modern Physics A 27, no. 05 (2012): 1230003. http://dx.doi.org/10.1142/s0217751x12300037.

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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 integrals of motion and the corresponding Lax pair are extracted based on algebraic considerations. Our attention is restricted to classical discrete and continuum integrable systems with periodic boundary conditions. Typical examples of discrete (Toda cha

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49

Zhao, Shiyin, Yufeng Zhang, and Jian Zhou. "Several Isospectral and Non-Isospectral Integrable Hierarchies of Evolution Equations." Symmetry 14, no. 2 (2022): 402. http://dx.doi.org/10.3390/sym14020402.

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By introducing a 3×3 matrix Lie algebra and employing the generalized Tu scheme, a AKNS isospectral–nonisospectral integrable hierarchy is generated by using a third-order matrix Lie algebra. Through a matrix transformation, we turn the 3×3 matrix Lie algebra into a 2×2 matrix case for which we conveniently enlarge it into two various expanding Lie algebras in order to obtain two different expanding integrable models of the isospectral–nonisospectral AKNS hierarchy by employing the integrable coupling theory. Specially, we propose a method for generating nonlinear integrable couplings for the

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50

COKER, DAVID A. "USE OF PROJECTORS FOR INTEGRABLE MODELS OF QUANTUM FIELD THEORY." International Journal of Modern Physics B 06, no. 17 (1992): 2893–911. http://dx.doi.org/10.1142/s0217979292002292.

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This paper is a discussion of the placement of integrable field theory models on a lattice of arbitrary spacing and the construction of the corresponding quantum integrals of motion. Two methods for producing local lattice models of both fundamental and nonfundamental types are covered. It is shown how projectors can be used to construct quasilocal lattice integrable models from quantum integrable field theories. The advantage of the projector method over other methods is the preservation of the original [Formula: see text]-matrix. The integrable structure of the model is then left unchanged a

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