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Journal articles on the topic 'Integrability'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Jarník, Jiří, and Jaroslav Kurzweil. "Pfeffer integrability does not imply $M_1$-integrability." Czechoslovak Mathematical Journal 44, no. 1 (1994): 47–56. http://dx.doi.org/10.21136/cmj.1994.128454.

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2

Schurle, Arlo W. "Perron Integrability Versus Lebesgue Integrability." Canadian Mathematical Bulletin 28, no. 4 (1985): 463–68. http://dx.doi.org/10.4153/cmb-1985-055-1.

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AbstractThe paper investigates the relationship between Perron - Stieltjes integrability and Lebesgue-Stieltjes integrability within the generalized Riemann approach. The main result states that with certain restrictions a Perron-Stieltjes integrable function is locally Lebesgue-Stieltjes integrable on an open dense set. This is then applied to show that a nonnegative Perron-Stieltjes integrable function is Lebesgue-Stieltjes integrable. Finally, measure theory is invoked to remove the restrictions in the main result.

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3

Mussardo, G. "Integrability, non-integrability and confinement." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 01 (2011): P01002. http://dx.doi.org/10.1088/1742-5468/2011/01/p01002.

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4

Kozak, A. V. "Integrability in AdS/CFT." Ukrainian Journal of Physics 58, no. 11 (2013): 1108–12. http://dx.doi.org/10.15407/ujpe58.11.1108.

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5

Bruno, Alexander D., and Alexander B. Batkhin. "Searching for New Integrals in the Euler–Poisson Equations." Axioms 14, no. 7 (2025): 484. https://doi.org/10.3390/axioms14070484.

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In the classical problem of the motion of a rigid body around a fixed point, which is described by the Euler–Poisson equations, we propose a new method for computing cases of integrability: first, we provide algorithms for computing values of parameters ensuring potential integrability, and then we select cases of global integrability. By this method we have obtained all the known cases of global integrability and six new cases of potential integrability for which the absence of their global integrability is proven.

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6

KUŚ, MAREK. "Integrability and non-integrability in quantum mechanics." Journal of Modern Optics 49, no. 12 (2002): 1979–85. http://dx.doi.org/10.1080/09500340210140759.

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7

Khesin, Boris, and Fedor Soloviev. "Non-integrability vs. integrability in pentagram maps." Journal of Geometry and Physics 87 (January 2015): 275–85. http://dx.doi.org/10.1016/j.geomphys.2014.07.027.

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8

M. Saadoune and R. Sayyad. "From Scalar McShane Integrability to Pettis Integrability." Real Analysis Exchange 38, no. 2 (2013): 445. http://dx.doi.org/10.14321/realanalexch.38.2.0445.

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9

Ünsal, Ömer, and Filiz Taşcan. "Soliton Solutions, Bäcklund Transformation and Lax Pair for Coupled Burgers System via Bell Polynomials." Zeitschrift für Naturforschung A 70, no. 5 (2015): 359–63. http://dx.doi.org/10.1515/zna-2015-0076.

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AbstractIn this work, we apply the binary Bell polynomial approach to coupled Burgers system. In other words, we investigate possible integrability of referred system. Bilinear form and soliton solutions are obtained, some figures related to these solutions are given. We also get Bäcklund transformations in both binary Bell polynomial form and bilinear form. Based on the Bäcklund transformation, Lax pair is obtained. Namely, this is a study in which integrabilitiy of coupled burgers system is investigated.

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10

Stefansson, Gunnar F. "Pettis Integrability." Transactions of the American Mathematical Society 330, no. 1 (1992): 401. http://dx.doi.org/10.2307/2154171.

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11

GAETA, GIUSEPPE. "QUATERNIONIC INTEGRABILITY." Journal of Nonlinear Mathematical Physics 18, no. 3 (2011): 461–74. http://dx.doi.org/10.1142/s1402925111001714.

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12

Stefánsson, Gunnar F. "Pettis integrability." Transactions of the American Mathematical Society 330, no. 1 (1992): 401–18. http://dx.doi.org/10.1090/s0002-9947-1992-1070352-0.

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13

TAMIZHMANI, K. M. "Integrability detectors." Pramana 85, no. 5 (2015): 823–47. http://dx.doi.org/10.1007/s12043-015-1105-6.

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14

Kruskal, M. D. "Analytic integrability." Physica D: Nonlinear Phenomena 28, no. 1-2 (1987): 227. http://dx.doi.org/10.1016/0167-2789(87)90153-9.

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15

Torrielli, Alessandro. "Classical integrability." Journal of Physics A: Mathematical and Theoretical 49, no. 32 (2016): 323001. http://dx.doi.org/10.1088/1751-8113/49/32/323001.

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16

Nepomechie, Rafael I. "Boundary integrability." Journal of Physics A: Mathematical and Theoretical 49, no. 42 (2016): 421004. http://dx.doi.org/10.1088/1751-8113/49/42/421004.

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17

Halburd, R. G. "Diophantine integrability." Journal of Physics A: Mathematical and General 38, no. 16 (2005): L263—L269. http://dx.doi.org/10.1088/0305-4470/38/16/l01.

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18

Verhulst, Ferdinand. "Integrability and Non-integrability of Hamiltonian Normal Forms." Acta Applicandae Mathematicae 137, no. 1 (2014): 253–72. http://dx.doi.org/10.1007/s10440-014-9998-5.

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19

Luzzatto, Stefano, Sina Tureli, and Khadim War. "Integrability of continuous bundles." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 752 (2019): 229–64. http://dx.doi.org/10.1515/crelle-2016-0049.

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Abstract We give new sufficient conditions for the integrability and unique integrability of continuous tangent subbundles on manifolds of arbitrary dimension, generalizing Frobenius’ classical theorem for {C^{1}} subbundles. Using these conditions, we derive new criteria for uniqueness of solutions to ODEs and PDEs and for the integrability of invariant bundles in dynamical systems. In particular, we give a novel proof of the Stable Manifold Theorem and prove some integrability results for dynamically defined dominated splittings.

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20

FIORANI, EMANUELE. "GEOMETRICAL ASPECTS OF INTEGRABLE SYSTEMS." International Journal of Geometric Methods in Modern Physics 05, no. 03 (2008): 457–71. http://dx.doi.org/10.1142/s0219887808002886.

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We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville–Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko–Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.

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21

Gao, Hongya, Yanjie Zhang, and Shuangli Li. "Integrability for Solutions of Anisotropic Obstacle Problems." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–6. http://dx.doi.org/10.1155/2012/549285.

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This paper deals with anisotropic obstacle problem for the𝒜-harmonic equation∑i=1nDi(ai(x,Du(x)))=0. An integrability result is given under suitable assumptions, which show higher integrability of the boundary datum, and the obstacle force solutionsuhave higher integrability as well.

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22

Jovanovic, Bozidar. "Symmetries and integrability." Publications de l'Institut Math?matique (Belgrade) 84, no. 98 (2008): 1–36. http://dx.doi.org/10.2298/pim0898001j.

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This is a survey on finite-dimensional integrable dynamical systems related to Hamiltonian G-actions. Within a framework of noncommutative integrability we study integrability of G-invariant systems, collective motions and reduced integrability. We also consider reductions of the Hamiltonian flows restricted to their invariant submanifolds generalizing classical Hess-Appel'rot case of a heavy rigid body motion.

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23

Kai, Tatsuya. "Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part I: Fundamental Properties and Integrability/Nonintegrability Conditions." Mathematical Problems in Engineering 2012 (2012): 1–32. http://dx.doi.org/10.1155/2012/543098.

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We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrability/nonintegrability. First, we give the definition ofA-rheonomous affine constraints and introduce, geometric representation their. Some fundamental properties of theA-rheonomous affine constrains are also derived. We next define the rheonomous bracket and derive some necessary and sufficient conditions on the respective three cases: complete integrability, partial integrability, and complete nonintegrability for theA-rheonomous affine constrains. Then, we apply the integrabi

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24

Algaba, Antonio, Cristóbal García, and Jaume Giné. "On the Formal Integrability Problem for Planar Differential Systems." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/482305.

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We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems inℂ2, and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.

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25

HANDS, D. WADE. "WHAT A DIFFERENCE A SUM (∑) MAKES: SUCCESS AND FAILURE IN THE RATIONALIZATION OF DEMAND." Journal of the History of Economic Thought 34, no. 3 (2012): 379–96. http://dx.doi.org/10.1017/s1053837212000387.

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This paper discusses the Sonnenschein–Mantel–Debreu (SMD) theorems in general equilibrium theory. It argues that the SMD results were related to the previous literature on the integrability of demand. The integrability question involved rationalizing individual demand functions, and the SMD theorems asked the same question about aggregate (market) excess demand functions. The paper’s two goals are to demonstrate how the SMD results followed naturally from the earlier work on integrability, and to point out that the profession’s reception was quite different; the integrability results were cons

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26

Li, Bo, and Na Ma. "Integrability Formulas. Part III." Formalized Mathematics 18, no. 2 (2010): 143–57. http://dx.doi.org/10.2478/v10037-010-0017-7.

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27

Chae, Dongho, and Jihoon Lee. "On Liouville type results for the stationary MHD in R 3." Nonlinearity 37, no. 9 (2024): 095006. http://dx.doi.org/10.1088/1361-6544/ad6128.

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Abstract This paper is concerned with the Liouville type theorems for the steady incompressible magnetohydrodynamics (MHD) equations. We establish that the solution to the steady MHD equations is identically zero under the integrability assumptions on (v, b). We show that, in particular, a combination of a strong integrability condition on the velocity of a fluid and a weak integrability condition on the magnetic field gives a sufficient condition on the Liouville type theorems. Furthermore, we show that the combination of the growth condition of the potential for the fluid velocity and the in

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28

Allami, M. "On Integrability of Christouâ€™s Sixth Order Solitary Wave Equations." Iraqi Journal of Science 60, no. 5 (2019): 1172–79. http://dx.doi.org/10.24996/ijs.2019.60.5.25.

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We examine the integrability in terms of PainlevÃ¨ analysis for several models of higher order nonlinear solitary wave equations which were recently derived by Christou. Our results point out that these equations do not possess PainlevÃ¨ property and fail the PainlevÃ¨ test for some special values of the coefficients; and that indicates a non-integrability criteria of the equations by means of the PainlevÃ¨ integrability.

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29

Nania, Luciana. "On some reverse integral inequalities." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 49, no. 2 (1990): 319–26. http://dx.doi.org/10.1017/s1446788700030597.

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30

Krippendorf, Sven, Dieter Lüst, and Marc Syvaeri. "Integrability Ex Machina." Fortschritte der Physik 69, no. 7 (2021): 2100057. http://dx.doi.org/10.1002/prop.202100057.

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31

Tanović-Miller. "NEW INTEGRABILITY CLASSES." Real Analysis Exchange 19, no. 1 (1993): 24. http://dx.doi.org/10.2307/44153792.

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32

Khesin, B., and S. Tabachnikov. "Contact complete integrability." Regular and Chaotic Dynamics 15, no. 4-5 (2010): 504–20. http://dx.doi.org/10.1134/s1560354710040076.

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33

Van Der Kamp, Peter H., and Jan A. Sanders. "On Testing Integrability." Journal of Nonlinear Mathematical Physics 8, no. 4 (2001): 561–74. http://dx.doi.org/10.2991/jnmp.2001.8.4.8.

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34

Kamp, Peter H. van der. "On proving integrability." Inverse Problems 18, no. 2 (2002): 405–14. http://dx.doi.org/10.1088/0266-5611/18/2/307.

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35

Eden, Burkhard, and Matthias Staudacher. "Integrability and transcendentality." Journal of Statistical Mechanics: Theory and Experiment 2006, no. 11 (2006): P11014. http://dx.doi.org/10.1088/1742-5468/2006/11/p11014.

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36

Tsiganov, Andrey V. "Rotations and Integrability." Regular and Chaotic Dynamics 29, no. 6 (2024): 913–30. https://doi.org/10.1134/s1560354724060029.

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AbstractWe discuss some families of integrable and superintegrable systems in $$n$$-dimensional Euclidean space which are invariant under $$m\geqslant n-2$$ rotations. The invariant Hamiltonian $$H=\sum p_{i}^{2}+V(q)$$ is integrable with $$n-2$$ integrals of motion $$M_{\alpha}$$ and an additional integral of motion $$G$$, which are first- and fourth-order polynomials in momenta, respectively.

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37

Luzzatto, Stefano, Sina Türeli, and Khadim Mbacke War. "Integrability ofC1invariant splittings." Dynamical Systems 31, no. 1 (2015): 79–88. http://dx.doi.org/10.1080/14689367.2015.1057480.

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38

Hietarinta, Jarmo. "Pure quantum integrability." Physics Letters A 246, no. 1-2 (1998): 97–104. http://dx.doi.org/10.1016/s0375-9601(98)00535-0.

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39

Evans, Jonathan M., and Jens Ole Madsen. "Integrability versus supersymmetry." Physics Letters B 389, no. 4 (1996): 665–72. http://dx.doi.org/10.1016/s0370-2693(96)80007-4.

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40

Murthy, Narayan S., Charles F. Osgood, and Oved Shisha. "On dominant integrability." Journal of Approximation Theory 51, no. 1 (1987): 89–92. http://dx.doi.org/10.1016/0021-9045(87)90098-0.

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41

Stolovitch, Laurent. "Singular complete integrability." Publications mathématiques de l'IHÉS 91, no. 1 (2000): 133–210. http://dx.doi.org/10.1007/bf02698742.

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42

Fokas, A. S. "Integrability and beyond." Journal of Mathematical Sciences 94, no. 4 (1999): 1593–99. http://dx.doi.org/10.1007/bf02365206.

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43

Franciosi, Michelangelo, and Gioconda Moscariello. "Higher integrability results." Manuscripta Mathematica 52, no. 1-3 (1985): 151–70. http://dx.doi.org/10.1007/bf01171490.

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44

Wojtkowski, Maciej P. "Integrability via reversibility." Journal of Geometry and Physics 115 (May 2017): 61–74. http://dx.doi.org/10.1016/j.geomphys.2016.07.015.

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45

Pucacco, Giuseppe, and Kjell Rosquist. "Energy dependent integrability." Journal of Geometry and Physics 115 (May 2017): 16–27. http://dx.doi.org/10.1016/j.geomphys.2016.10.001.

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46

Gutkin, E. "Integrability without formulas." Physica D: Nonlinear Phenomena 28, no. 1-2 (1987): 243. http://dx.doi.org/10.1016/0167-2789(87)90193-x.

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47

Boos, H., F. Göhmann, A. Klümper, Kh S. Nirov, and A. V. Razumov. "Universal integrability objects." Theoretical and Mathematical Physics 174, no. 1 (2013): 21–39. http://dx.doi.org/10.1007/s11232-013-0002-8.

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48

Basse-O'Connor, Andreas. "Integrability of Seminorms." Electronic Journal of Probability 16 (2011): 216–29. http://dx.doi.org/10.1214/ejp.v16-853.

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49

Andrews, Kevin T. "Universal Pettis Integrability." Canadian Journal of Mathematics 37, no. 1 (1985): 141–59. http://dx.doi.org/10.4153/cjm-1985-011-5.

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Since the invention of the Pettis integral over forty years ago [11], the problem of recognizing the Pettis integrability of a function against an individual measure has been much studied [5, 6, 7, 8, 9, 20]. More recently, Riddle-Saab-Uhl [14] and Riddle-Saab [13] have considered the problem of when a function is integrable against every Radon measure on a fixed compact Hausdorff space. These papers give various sufficient conditions on a function that ensure this universal Pettis integrability. In this paper, we see how far these various conditions go toward characterizing universal Pettis i

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50

Fernandes, Rui Loja, and Daan Michiels. "Associativity and integrability." Transactions of the American Mathematical Society 373, no. 7 (2020): 5057–110. http://dx.doi.org/10.1090/tran/8073.

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