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Journal articles on the topic 'Integrable'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Álvarez Merino, Paula, Carmen Requena Hernández, and Francisco Salto Alemany. "LA INTEGRACIÓN MÁS QUE LA EDAD INFLUYE EN EL RENDIMIENTO DEL RAZONAMIENTO DEDUCTIVO." International Journal of Developmental and Educational Psychology. Revista INFAD de Psicología. 1, no. 2 (2016): 221. http://dx.doi.org/10.17060/ijodaep.2016.n2.v1.569.

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Abstract.This work merges from our interest for the evolution of deductive reasoning across the life cycle from youth to older age. With time, reasoning resources seem to be compromised and constrained, even if on the other side they seem more flexible. The literature on deductive reasoning considers that deduction only takes place between integrable premisses, that is, premisses whose elements share any categorematical term. The present research designed, applied and analyzed an instrument to measure deduction. The measure is based on integration as a general rule to deduce a conclusion from

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2

Kai, Tatsuya. "Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part II: Foliation Structures and Integrating Algorithms." Mathematical Problems in Engineering 2012 (2012): 1–34. http://dx.doi.org/10.1155/2012/345942.

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This paper investigates foliation structures of configuration manifolds and develops integrating algorithms for a class of constraints that contain the time variable, calledA-rheonomous affine constrains. We first present some preliminaries on theA-rheonomous affine constrains. Next, theoretical analysis on foliation structures of configuration manifolds is done for the respective three cases where theA-rheonomous affine constrains are completely integrable, partially integrable, and completely nonintegrable. We then propose two types of integrating algorithms in order to calculate independent

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3

Mañas, Manuel. "From integrable nets to integrable lattices." Journal of Mathematical Physics 43, no. 5 (2002): 2523. http://dx.doi.org/10.1063/1.1454185.

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4

Maciejewski, Andrzej J., and Maria Przybylska. "Integrable deformations of integrable Hamiltonian systems." Physics Letters A 376, no. 2 (2011): 80–93. http://dx.doi.org/10.1016/j.physleta.2011.10.031.

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5

Xia, Baoqiang, and Ruguang Zhou. "Integrable deformations of integrable symplectic maps." Physics Letters A 373, no. 47 (2009): 4360–67. http://dx.doi.org/10.1016/j.physleta.2009.09.063.

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6

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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7

ZHU, LI, HONGWEI YANG, and HUANHE DONG. "A LIOUVILLE INTEGRABLE MULTI-COMPONENT INTEGRABLE SYSTEM AND ITS INTEGRABLE COUPLINGS." International Journal of Modern Physics B 24, no. 08 (2010): 1021–46. http://dx.doi.org/10.1142/s0217979209053667.

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A Liouville integrable multi-component integrable system is obtained by the vector loop algebra. Then, the integrable couplings of the above system are presented by using the expanding vector loop algebra [Formula: see text] of the [Formula: see text]. Finally, the bi -Hamiltonian structure of the obtained system is given, respectively, by the variational identity.

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8

Bountis, Tassos, Zhanat Zhunussova, Karlygash Dosmagulova, and George Kanellopoulos. "Integrable and non-integrable Lotka-Volterra systems." Physics Letters A 402 (June 2021): 127360. http://dx.doi.org/10.1016/j.physleta.2021.127360.

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9

Olshanetsky, M. A. "Integrable extensions of classical elliptic integrable systems." Theoretical and Mathematical Physics 208, no. 2 (2021): 1061–74. http://dx.doi.org/10.1134/s0040577921080067.

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10

Výborný. "KURZWEIL-HENSTOCK ABSOLUTE INTEGRABLE MEANS McSHANE INTEGRABLE." Real Analysis Exchange 20, no. 1 (1994): 363. http://dx.doi.org/10.2307/44152498.

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11

Maciejewski, Andrzej J., and Maria Przybylska. "Integrable variational equations of non-integrable systems." Regular and Chaotic Dynamics 17, no. 3-4 (2012): 337–58. http://dx.doi.org/10.1134/s1560354712030094.

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12

Zhu, Li. "Discrete integrable system and its integrable coupling." Chinese Physics B 18, no. 3 (2009): 850–55. http://dx.doi.org/10.1088/1674-1056/18/3/002.

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13

Zhu, Li. "Liouville Integrable System and Associated Integrable Coupling." Communications in Theoretical Physics 52, no. 6 (2009): 987–91. http://dx.doi.org/10.1088/0253-6102/52/6/03.

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14

Papageorgiou, V. G., F. W. Nijhoff, and H. W. Capel. "Integrable mappings and nonlinear integrable lattice equations." Physics Letters A 147, no. 2-3 (1990): 106–14. http://dx.doi.org/10.1016/0375-9601(90)90876-p.

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15

Lăzureanu, Cristian, Ciprian Hedrea, and Camelia Petrişor. "On the integrable deformations of a system related to the motion of two vortices in an ideal incompressible fluid." ITM Web of Conferences 29 (2019): 01015. http://dx.doi.org/10.1051/itmconf/20192901015.

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Altering the first integrals of an integrable system integrable deformations of the given system are obtained. These integrable deformations are also integrable systems, and they generalize the initial system. In this paper we give a method to construct integrable deformations of maximally superintegrable Hamiltonian mechanical systems with two degrees of freedom. An integrable deformation of a maximally superintegrable Hamiltonian mechanical system preserves the number of first integrals, but is not a Hamiltonian mechanical system, generally. We construct integrable deformations of the maxima

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16

Zhang, Jian, Chiping Zhang, and Yunan Cui. "Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with SO(4)." Open Mathematics 15, no. 1 (2017): 203–17. http://dx.doi.org/10.1515/math-2017-0017.

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Abstract In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated with SO(4) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities.

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17

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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18

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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19

Veselov, A. P. "Integrable maps." Russian Mathematical Surveys 46, no. 5 (1991): 1–51. http://dx.doi.org/10.1070/rm1991v046n05abeh002856.

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20

Bobenko, A. I. "Integrable surfaces." Functional Analysis and Its Applications 24, no. 3 (1991): 227–28. http://dx.doi.org/10.1007/bf01077966.

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21

Berenstein, Arkady, Jacob Greenstein, and David Kazhdan. "Integrable clusters." Comptes Rendus Mathematique 353, no. 5 (2015): 387–90. http://dx.doi.org/10.1016/j.crma.2015.02.006.

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22

Marikhin, V. G., and A. B. Shabat. "Integrable lattices." Theoretical and Mathematical Physics 118, no. 2 (1999): 173–82. http://dx.doi.org/10.1007/bf02557310.

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23

Sorensen, E. S., S. Eggert, and I. Affleck. "Integrable versus non-integrable spin chain impurity models." Journal of Physics A: Mathematical and General 26, no. 23 (1993): 6757–76. http://dx.doi.org/10.1088/0305-4470/26/23/023.

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24

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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25

José Mendoza. "Which Integrable Functions Fail to be Absolutely Integrable?" Real Analysis Exchange 43, no. 1 (2018): 243. http://dx.doi.org/10.14321/realanalexch.43.1.0243.

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26

Wang, Haifeng, and Yufeng Zhang. "Two Nonisospectral Integrable Hierarchies and its Integrable Coupling." International Journal of Theoretical Physics 59, no. 8 (2020): 2529–39. http://dx.doi.org/10.1007/s10773-020-04519-9.

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27

Agricola, Ilka, Simon G. Chiossi, and Anna Fino. "Solvmanifolds with integrable and non-integrable G2 structures." Differential Geometry and its Applications 25, no. 2 (2007): 125–35. http://dx.doi.org/10.1016/j.difgeo.2006.05.002.

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28

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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29

Hu, Beibei, and Tiecheng Xia. "The Binary Nonlinearization of the Super Integrable System and Its Self-Consistent Sources." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 3-4 (2017): 285–92. http://dx.doi.org/10.1515/ijnsns-2016-0158.

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AbstractThe super integrable system and its super Hamiltonian structure are established based on a loop super Lie algebra and super-trace identity in this paper. Then the super integrable system with self-consistent sources and conservation laws of the super integrable system are constructed. Furthermore, an explicit Bargmann symmetry constraint and the binary nonlinearization of Lax pairs for the super integrable system are established. Under the symmetry constraint,the $n$-th flow of the super integrable system is decomposed into two super finite-dimensional integrable Hamilton systems over

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30

Wang, Haifeng, and Yufeng Zhang. "Generating of Nonisospectral Integrable Hierarchies via the Lie-Algebraic Recursion Scheme." Mathematics 8, no. 4 (2020): 621. http://dx.doi.org/10.3390/math8040621.

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In the paper, we introduce an efficient method for generating non-isospectral integrable hierarchies, which can be used to derive a great many non-isospectral integrable hierarchies. Based on the scheme, we derive a non-isospectral integrable hierarchy by using Lie algebra and the corresponding loop algebra. It follows that some symmetries of the non-isospectral integrable hierarchy are also studied. Additionally, we also obtain a few conserved quantities of the isospectral integrable hierarchies.

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31

XU, XI-XIANG, and HONG-XIANG YANG. "A FAMILY OF DISCRETE INTEGRABLE COUPLING SYSTEMS AND ITS LIOUVILLE INTEGRABILITY." Modern Physics Letters B 23, no. 13 (2009): 1671–85. http://dx.doi.org/10.1142/s0217984909019843.

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A discrete matrix spectral problem and corresponding family of discrete integrable systems are discussed. A semi-direct sum of Lie algebras of four-by-four matrices is introduced, and the related integrable coupling systems of resulting discrete integrable systems are derived. The obtained discrete integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, Liouville integrability of the family of obtained integrable coupling systems is demonstrated.

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32

Ma, Wen-Xiu. "Integrable Nonlocal PT-Symmetric Modified Korteweg-de Vries Equations Associated with so(3, \({\mathbb{R}}\))." Symmetry 13, no. 11 (2021): 2205. http://dx.doi.org/10.3390/sym13112205.

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We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra so(3,R). The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal complex reverse-spacetime and real reverse-spacetime modified Korteweg-de Vries equations associated with so(3,R).

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33

Li, Yuqing, Huanhe Dong, and Baoshu Yin. "A Hierarchy of Discrete Integrable Coupling System with Self-Consistent Sources." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/416472.

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Integrable coupling system of a lattice soliton equation hierarchy is deduced. The Hamiltonian structure of the integrable coupling is constructed by using the discrete quadratic-form identity. The Liouville integrability of the integrable coupling is demonstrated. Finally, the discrete integrable coupling system with self-consistent sources is deduced.

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34

Newton, Paul K., and Bharat Khushalani. "Integrable decomposition methods and ensemble averaging for non-integrableN-vortex problems." Journal of Turbulence 3 (January 2002): N54. http://dx.doi.org/10.1088/1468-5248/3/1/054.

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35

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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36

Piazza, Luisa Di, and Kazimierz Musiał. "Decompositions of Weakly Compact Valued Integrable Multifunctions." Mathematics 8, no. 6 (2020): 863. http://dx.doi.org/10.3390/math8060863.

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We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it

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37

Combot, Thierry, Andrzej J. Maciejewski, and Maria Przybylska. "Integrability of the generalised Hill problem." Nonlinear Dynamics 107, no. 3 (2021): 1989–2002. http://dx.doi.org/10.1007/s11071-021-07040-8.

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AbstractWe consider a certain two-parameter generalisation of the planar Hill lunar problem. We prove that for nonzero values of these parameters the system is not integrable in the Liouville sense. For special choices of parameters the system coincides with the classical Hill system, the integrable synodical Kepler problem or the integrable parametric Hénon system. We prove that the synodical Kepler problem is not super-integrable, and that the parametric Hénon problem is super-integrable for infinitely many values of the parameter.

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38

Li, Chuanzhong. "Constrained lattice-field hierarchies and Toda system with Block symmetry." International Journal of Geometric Methods in Modern Physics 13, no. 05 (2016): 1650061. http://dx.doi.org/10.1142/s0219887816500614.

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In this paper, we construct the additional [Formula: see text]-symmetry and ghost symmetry of two-lattice field integrable hierarchies. Using the symmetry constraint, we construct constrained two-lattice integrable systems which contain several new integrable difference equations. Under a further reduction, the constrained two-lattice integrable systems can be combined into one single integrable system, namely the well-known one-dimensional original Toda hierarchy. We prove that the one-dimensional original Toda hierarchy has a nice Block Lie symmetry.

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39

Yu, Fajun, Shuo Feng, and Yanyu Zhao. "A Complex Integrable Hierarchy and Its Hamiltonian Structure for Integrable Couplings of WKI Soliton Hierarchy." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/146537.

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We generate complex integrable couplings from zero curvature equations associated with matrix spectral problems in this paper. A direct application to the WKI spectral problem leads to a novel soliton equation hierarchy of integrable coupling system; then we consider the Hamiltonian structure of the integrable coupling system. We select theU¯,V¯and generate the nonlinear composite parts, which generate new extended WKI integrable couplings. It is also indicated that the method of block matrix is an efficient and straightforward way to construct the integrable coupling system.

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40

Ma, Wen-Xiu. "Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)". Proceedings of the American Mathematical Society, Series B 9, № 1 (2022): 1–11. http://dx.doi.org/10.1090/bproc/116.

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We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) . The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal reverse-space, reverse-time and reverse-spacetime nonlinear Schrödinger equations associated with so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) .

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41

Zhang, Li-Qin, та Wen-Xiu Ma. "Nonlocal PT-Symmetric Integrable Equations of Fourth-Order Associated with so(3, ℝ)". Mathematics 9, № 17 (2021): 2130. http://dx.doi.org/10.3390/math9172130.

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The paper aims to construct nonlocal PT-symmetric integrable equations of fourth-order, from nonlocal integrable reductions of a fourth-order integrable system associated with the Lie algebra so(3,R). The nonlocalities involved are reverse-space, reverse-time, and reverse-spacetime. All of the resulting nonlocal integrable equations possess infinitely many symmetries and conservation laws.

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42

Huseynli, A. F. "The A-integral and Calderon-Zygmund operators." Baku Mathematical Journal 3, no. 2 (2024): 163–73. http://dx.doi.org/10.32010/j.bmj.2024.16.

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It is known that the function obtained by the action of the Calderon-Zygmund operator on a Lebesgue integrable function can be non-Lebesgue integrable. In this paper, we prove that the function obtained by the action of the Calderon-Zygmund operator on a Lebesgue integrable function is A-integrable and derive an analogue of the Riesz equality.

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43

Zhang, Jian, Chiping Zhang, and Yunan Cui. "Bi-Integrable and Tri-Integrable Couplings of a Soliton Hierarchy Associated with SO(3)." Advances in Mathematical Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/9743475.

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Based on the three-dimensional real special orthogonal Lie algebra SO(3), by zero curvature equation, we present bi-integrable and tri-integrable couplings associated with SO(3) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by applying the variational identities.

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44

Racca, Abraham Perral, and Emmanuel A. Cabral. "The N-Integral." Journal of the Indonesian Mathematical Society 26, no. 2 (2020): 242–57. http://dx.doi.org/10.22342/jims.26.2.865.242-257.

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In this paper, we introduced a Henstock-type integral named N-integral of a real valued function f on a closed and bounded interval [a,b]. The set N-integrable functions lie entirely between Riemann integrable functions and Henstock-Kurzweil integrable functions. Furthermore, this new integral integrates all improper Riemann integrable functions even if they are not Lebesgue integrable. It was shown that for a Henstock-Kurzweil integrable function f on [a,b], the following are equivalent:The function f is N-integrable;There exists a null set S for which given epsilon 0 there exists a gauge del

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45

Balasubramanian, Vijay, Rathindra Nath Das, Johanna Erdmenger, and Zhuo-Yu Xian. "Chaos and integrability in triangular billiards." Journal of Statistical Mechanics: Theory and Experiment 2025, no. 3 (2025): 033202. https://doi.org/10.1088/1742-5468/adba41.

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Abstract We characterize quantum dynamics in triangular billiards in terms of five properties: (1) the level spacing ratio (LSR), (2) spectral complexity (SC), (3) Lanczos coefficient variance, (4) energy eigenstate localisation in the Krylov basis, and (5) dynamical growth of spread complexity. The billiards we study are classified as integrable, pseudointegrable or non-integrable, depending on their internal angles which determine properties of classical trajectories and associated quantum spectral statistics. A consistent picture emerges when transitioning from integrable to non-integrable

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46

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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47

Nonnenmacher, D. J. F. "Every ${\rm M}\sb1$-integrable function is Pfeffer integrable." Czechoslovak Mathematical Journal 43, no. 2 (1993): 327–30. http://dx.doi.org/10.21136/cmj.1993.128400.

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48

Tao, Sixing. "Nonlinear Super Integrable Couplings of a Super Integrable Hierarchy." Journal of Applied Mathematics and Physics 04, no. 04 (2016): 648–54. http://dx.doi.org/10.4236/jamp.2016.44074.

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49

Chang, Hui, and Yuxia Li. "Two New Integrable Hierarchies and Their Nonlinear Integrable Couplings." Journal of Applied Mathematics and Physics 06, no. 06 (2018): 1346–62. http://dx.doi.org/10.4236/jamp.2018.66113.

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50

Xiao-Hong, Chen, Xia Tie-Cheng, and Zhu Lian-Cheng. "An integrable Hamiltonian hierarchy and associated integrable couplings system." Chinese Physics 16, no. 9 (2007): 2493–97. http://dx.doi.org/10.1088/1009-1963/16/9/001.

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