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Journal articles on the topic 'Lax representation'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

BRUNELLI, J. C., M. GÜRSES, and K. ZHELTUKHIN. "ON THE INTEGRABILITY OF A CLASS OF MONGE–AMPÈRE EQUATIONS." Reviews in Mathematical Physics 13, no. 04 (2001): 529–43. http://dx.doi.org/10.1142/s0129055x01000764.

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We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge–Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge–Ampère equations. Local as well nonlocal conserved densities are obtained.

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2

Das, Ashok, and Ziemowit Popowicz. "Supersymmetric Moyal-Lax representation." Journal of Physics A: Mathematical and General 34, no. 31 (2001): 6105–17. http://dx.doi.org/10.1088/0305-4470/34/31/305.

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3

Cieśliński, Jan L., and Artur Kobus. "Lax Triples for Integrable Surfaces in Three-Dimensional Space." Advances in Mathematical Physics 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/8386420.

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We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean spaceE3. We begin with a natural integrable deformation of the principal chiral model. Then, we show that all deformations linear in the spectral parameterλare trivial unless we admit Lax representations in a larger space. We present an explicit example of triply orthogonal systems with Lax representation in the groupSpin(6). Finally, the obtained results are interpreted in the context of the soliton surfaces approach.

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4

Rosensteel, G. "Lax representation of Riemann ellipsoids." Applied Mathematics Letters 6, no. 3 (1993): 55–58. http://dx.doi.org/10.1016/0893-9659(93)90034-k.

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5

Das, Ashok, and Ziemowit Popowicz. "Properties of Moyal–Lax representation." Physics Letters B 510, no. 1-4 (2001): 264–70. http://dx.doi.org/10.1016/s0370-2693(01)00561-5.

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6

Steeb, W.-H., Y. Hardy, and R. Stoop. "Lax Representation and Kronecker Product." Physica Scripta 67, no. 6 (2003): 464–65. http://dx.doi.org/10.1238/physica.regular.067a00464.

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7

Steeb, W. H., and Lai Choy Heng. "Lax representation and Kronecker product." International Journal of Theoretical Physics 35, no. 3 (1996): 475–79. http://dx.doi.org/10.1007/bf02082817.

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8

Balandin, Alexander V. "Tensor fields associated with integrable systems of chiral." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 21, no. 4 (2019): 405–12. http://dx.doi.org/10.15507/2079-6900.21.201904.405-412.

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This article describes necessary conditions for chiral-type systems to admit Lax representation with values in simple compact Lie algebras. These conditions state that there exists a covariant constant tensor field with an additional property. It is proposed to construct in an invariant way some covariant tensor fields using the Lax representation of the system under consideration. These fields are constructed by taking linear differential forms with values in the Lie algebra that are constructed using the Lax representation of the system and substituting them into an arbitrary Ad-invariant fo

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9

Pöchtrager, Markus A. "Tense? (Re)lax!" Acta Linguistica Academica 67, no. 1 (2020): 53–71. http://dx.doi.org/10.1556/2062.2020.00005.

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AbstractThis article looks at what is referred to as the tense/lax contrast in English and proposes that members of the two sets of vowel have the same basic structure but differ in how part of that structure is made use of by its neighbours. The proposal forms part of a general theory of the representation of vowel height within the framework of Government Phonology 2.0.

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10

Tsiganov, A. V. "The Kowalewski top: A new Lax representation." Journal of Mathematical Physics 38, no. 1 (1997): 196–211. http://dx.doi.org/10.1063/1.531850.

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11

Zheltukhin, K. "Recursion operator and dispersionless rational Lax representation." Physics Letters A 297, no. 5-6 (2002): 402–7. http://dx.doi.org/10.1016/s0375-9601(02)00374-2.

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12

IVAN, GHEORGHE, and MIHAI IVAN. "GENERAL EULER TOP SYSTEM AND ITS LAX REPRESENTATION." International Journal of Geometric Methods in Modern Physics 08, no. 05 (2011): 937–44. http://dx.doi.org/10.1142/s0219887811005543.

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13

Scharinger, Mathias, Philip J. Monahan, and William J. Idsardi. "Asymmetries in the Processing of Vowel Height." Journal of Speech, Language, and Hearing Research 55, no. 3 (2012): 903–18. http://dx.doi.org/10.1044/1092-4388(2011/11-0065).

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Purpose Speech perception can be described as the transformation of continuous acoustic information into discrete memory representations. Therefore, research on neural representations of speech sounds is particularly important for a better understanding of this transformation. Speech perception models make specific assumptions regarding the representation of mid vowels (e.g., [ɛ]) that are articulated with a neutral position in regard to height. One hypothesis is that their representation is less specific than the representation of vowels with a more specific position (e.g., [æ]). Method In a

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14

Steeb, W. H., and A. J. van Tonder. "A NOTE ON FIRST INTEGRALS AND LAX REPRESENTATION." Quaestiones Mathematicae 11, no. 3 (1988): 301–5. http://dx.doi.org/10.1080/16073606.1988.9632146.

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15

Gürses, Metin, Atalay Karasu, and Vladimir V. Sokolov. "On construction of recursion operators from Lax representation." Journal of Mathematical Physics 40, no. 12 (1999): 6473–90. http://dx.doi.org/10.1063/1.533102.

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16

Brunelli, J. C., and Ashok Das. "A Lax representation for the Born-Infeld equation." Physics Letters B 426, no. 1-2 (1998): 57–63. http://dx.doi.org/10.1016/s0370-2693(98)00265-2.

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17

Balandin, A. V., O. N. Pakhareva, and G. V. Potyomin. "Lax representation of the chiral-type field equations." Physics Letters A 283, no. 3-4 (2001): 168–76. http://dx.doi.org/10.1016/s0375-9601(01)00214-6.

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18

Fioravanti, Davide, and Rafael I. Nepomechie. "An inhomogeneous Lax representation for the Hirota equation." Journal of Physics A: Mathematical and Theoretical 50, no. 5 (2017): 054001. http://dx.doi.org/10.1088/1751-8121/aa5303.

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19

Myrzakulova, Zh R., K. R. Yesmakhanova, and Zh S. Zhubayeva. "EQUIVALENCE OF THE HUNTER-SAXON EQUATION AND THE GENERALIZED HEISENBERG FERROMAGNET EQUATION." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (2021): 33–38. http://dx.doi.org/10.32014/2021.2518-1726.18.

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Integrable systems play an important role in modern mathematics, theoretical and mathematical physics. The display of integrable equations with exact solutions and some special solutions can provide important guarantees for the analysis of its various properties. The Hunter-Saxton equation belongs to the family of integrable systems. The extensive and interesting mathematical theory, underlying the Hunter-Saxton equation, creates active mathematical and physical research. The Hunter-Saxton equation (HSE) is a high-frequency limit of the famous Camassa-Holm equation. The physical interpretation

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20

Karabanov, A. "Tensor extensions of Lax equations." Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences, no. 4 (September 21, 2023): 5–9. http://dx.doi.org/10.19110/1994-5655-2023-4-5-9.

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The Lax equations dL/dt = [M,L] play an important role in the integrability theory of nonlinear evolution equations and quantum dynamics. In this work, tensor extensions of the Lax equations are suggested with M : V → V and L : Tk(V ) → V , k = 1, 2, . . ., on a complex vector space V . These extensions belong to the generalised class of Lax equations (introduced earlier by Bordemann) dL/dt = ρk(M)L where ρk is a representation of a Lie algebra. The case k = 1, ρ1 = ad corresponds to the usual Lax equations. The extended Lax pairs are studi

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21

Zeng, Yunbo, and Yishen Li. "The deduction of the Lax representation for constrained flows from the adjoint representation." Journal of Physics A: Mathematical and General 26, no. 5 (1993): L273—L278. http://dx.doi.org/10.1088/0305-4470/26/5/018.

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22

Falqui, Gregorio. "Lax representation and Poisson geometry of the Kowalevski top." Journal of Physics A: Mathematical and General 34, no. 11 (2001): 2077–85. http://dx.doi.org/10.1088/0305-4470/34/11/301.

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23

Piskunov, A. S. "A (3+1)-DIMENSIONAL EQUATION ADMITTING A LAX REPRESENTATION." Russian Academy of Sciences. Izvestiya Mathematics 40, no. 1 (1993): 225–33. http://dx.doi.org/10.1070/im1993v040n01abeh001865.

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24

Yu, Jing, and Jingwei Han. "Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/507540.

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Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation andr-matrix are also given in this paper.

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25

Bracken, Paul. "Quaternionic representation of the moving frame for surfaces in Euclidean three-space and Lax pair." International Journal of Mathematics and Mathematical Sciences 2004, no. 15 (2004): 755–62. http://dx.doi.org/10.1155/s0161171204310392.

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The moving frame and associated Gauss-Codazzi equations for surfaces in three-space are introduced. A quaternionic representation is used to identify the Gauss-Weingarten equation with a particular Lax representation. Several examples are given, such as the case of constant mean curvature.

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26

Zeng, Yunbo. "HOW TO CONSTRUCT LAX REPRESENTATION FOR CONSTRAINED FLOWS OF THE BOUSSINESQ HIERARCHY VIA ADJOINT REPRESENTATIONS." Acta Mathematica Scientia 17, no. 1 (1997): 97–107. http://dx.doi.org/10.1016/s0252-9602(17)30681-1.

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27

Guha, P., S. Garai, and A. G. Choudhury. "Lax Pairs and First Integrals for Autonomous and Non-Autonomous Differential Equations Belonging to the Painlevé – Gambier List." Nelineinaya Dinamika 16, no. 4 (2020): 637–50. http://dx.doi.org/10.20537/nd200408.

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Recently Sinelshchikov et al. [1] formulated a Lax representation for a family of nonautonomous second-order differential equations. In this paper we extend their result and obtain the Lax pair and the associated first integral of a non-autonomous version of the Levinson – Smith equation. In addition, we have obtained Lax pairs and first integrals for several equations of the Painlevé – Gambier list, namely, the autonomous equations numbered XII, XVII, XVIII, XIX, XXI, XXII, XXIII, XXIX, XXXII, XXXVII, XLI, XLIII, as well as the non-autonomous equations Nos. XV and XVI in Ince’s book.

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28

UVAROV, D. V. "ON INTEGRABILITY OF MASSLESS AdS4×ℂℙ3 SUPERPARTICLE EQUATIONS". Modern Physics Letters A 29, № 01 (2014): 1350183. http://dx.doi.org/10.1142/s0217732313501836.

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29

LEVAN, NHAN, and CARLOS S. KUBRUSLY. "UNITARY EQUIVALENCE AND TRANSLATION REPRESENTATION IN WAVELET THEORY." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 02 (2012): 1250019. http://dx.doi.org/10.1142/s0219691312500191.

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Unitary Equivalence and Translation Representation play a key role in the Lax–Phillips Scattering Theory. In this paper we show that Translation Representation also plays an important role in Wavelet Theory, for Discrete Multi-Resolution Approximation as well as for Continuous Multi-Translation Approximation — to be defined in the paper.

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30

Bobenko, A. I., and V. B. Kuznetsov. "Lax representation and new formulae for the Goryachev-Chaplygin top." Journal of Physics A: Mathematical and General 21, no. 9 (1988): 1999–2006. http://dx.doi.org/10.1088/0305-4470/21/9/016.

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31

Avan, J., J. M. Maillard, and M. Talon. "The Adler-van Moerbeke model. Lax representation and poisson structure." Physics Letters B 240, no. 1-2 (1990): 145–48. http://dx.doi.org/10.1016/0370-2693(90)90423-4.

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32

Antonowicz, M., and S. Rauch-Wojciechowski. "Soliton hierarchies with sources and Lax representation for restricted flows." Inverse Problems 9, no. 2 (1993): 201–15. http://dx.doi.org/10.1088/0266-5611/9/2/003.

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33

Zheltukhin, Kostyantyn V. "Recursion operator for a system with non-rational Lax representation." Ufimskii Matematicheskii Zhurnal 8, no. 2 (2016): 112–18. http://dx.doi.org/10.13108/2016-8-2-112.

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34

González-Prieto, Ángel, Marina Logares, and Vicente Muñoz. "A lax monoidal topological quantum field theory for representation varieties." Bulletin des Sciences Mathématiques 161 (July 2020): 102871. http://dx.doi.org/10.1016/j.bulsci.2020.102871.

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35

Enolskii, V. Z., and M. Salerno. "Lax representation for two-particle dynamics splitting on two tori." Journal of Physics A: Mathematical and General 29, no. 17 (1996): L425—L431. http://dx.doi.org/10.1088/0305-4470/29/17/002.

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36

Kondrat'ev, A. Yu, and V. Z. �nol'skii. "Jacobi polynomials and Lax representation for completely integrable dynamical systems." Ukrainian Mathematical Journal 46, no. 8 (1994): 1198–201. http://dx.doi.org/10.1007/bf01056181.

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37

Berntson, Bjorn K., Edwin Langmann, and Jonatan Lenells. "On the non-chiral intermediate long wave equation." Nonlinearity 35, no. 8 (2022): 4549–84. http://dx.doi.org/10.1088/1361-6544/ac45e8.

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Abstract We study integrability properties of the non-chiral intermediate long wave equation recently introduced by the authors as a parity-invariant variant of the intermediate long wave equation. For this new equation we: (a) derive a Lax pair, (b) derive a Hirota bilinear form, (c) derive a Bäcklund transformation, (d) use, separately, the Bäcklund transformation and the Lax representation to obtain an infinite number of conservation laws.

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38

ARATYN, HENRIK, and ASHOK DAS. "THE sAKNS HIERARCHY." Modern Physics Letters A 13, no. 15 (1998): 1185–99. http://dx.doi.org/10.1142/s0217732398001261.

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We study, systematically, the properties of the supersymmetric AKNS (sAKNS) hierarchy. In particular, we discuss the Lax representation in terms of a bosonic Lax operator and some special features of the equations and construct the bosonic local charges as well as the fermionic nonlocal charges associated with the system starting from the Lax operator. We obtain the Hamiltonian structures of the system and check the Jacobi identity through the method of prolongation. We also show that this hierarchy of equations can equivalently be described in terms of a fermionic Lax operator. We obtain the

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39

Osipov, Andrey. "Inverse spectral problem for Jacobi operators and Miura transformation." Concrete Operators 8, no. 1 (2021): 77–89. http://dx.doi.org/10.1515/conop-2020-0116.

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Abstract We study a Miura-type transformation between Kac - van Moerbeke (Volterra) and Toda lattices in terms of the inverse spectral problem for Jacobi operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the moments of its Weyl function, can be used in solving initial-boundary value problem for both systems. It is shown that the Miura transformation can be easily described in terms of these moments. Using this description we establish a bijection between the Volterra lattices and the class of To

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40

Xu, Xi-Xiang, and Ye-Peng Sun. "Mukherjee–Choudhury–Chowdhury spectral problem and the semi-discrete integrable system." International Journal of Modern Physics B 30, no. 28n29 (2016): 1640027. http://dx.doi.org/10.1142/s0217979216400270.

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Starting from the Mukherjee–Choudhury–Chowdhury spectral problem, we derive a semi-discrete integrable system by a proper time spectral problem. A Bäcklund transformation of Darboux type of this system is established with the help of gauge transformation of the Lax pairs. By means of the obtained Bäcklund transformation, an exact solution is given. Moreover, Hamiltonian form of this system is constructed. Further, through a constraint of potentials and eigenfunctions, the Lax pair and the adjoint Lax pair of the obtained semi-discrete integrable system are nonlinearized as an integrable symple

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41

Bracken, Paul. "Classically Integrable Non-Linear Sigma Models and their Geometric Properties." Journal of Geometry and Symmetry in Physics 59 (2021): 47–65. http://dx.doi.org/10.7546/jgsp-59-2021-47-65.

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General classes of non-linear sigma models originating from a specified action are developed and studied. Models can be grouped and considered within a single mathematical structure this way. The geometrical properties of these models and the theories they describe are developed in detail. The zero curvature representation of the equations of motion are found. Those representations which have a spectral parameter are of importance here. Some new models with Lax pairs which depend on a spectral parameter are found. Some particular classes of solutions are worked out and discussed.

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42

Mahmood, Irfan, and Muhammad Waseem. "Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation." Advances in Mathematical Physics 2021 (January 15, 2021): 1–5. http://dx.doi.org/10.1155/2021/8851043.

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In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the N -th form in terms of Wranskian.

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43

Zhu, Zuonong, Hongci Huang, and Weimin Xue. "New Lax Representation and Integrable Discretization of the Relativistic Volterra Lattice." Journal of the Physical Society of Japan 68, no. 3 (1999): 771–75. http://dx.doi.org/10.1143/jpsj.68.771.

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44

Grundland, A. M., and S. Post. "Soliton surfaces associated with symmetries of ODEs written in Lax representation." Journal of Physics: Conference Series 343 (February 8, 2012): 012044. http://dx.doi.org/10.1088/1742-6596/343/1/012044.

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45

Bogoyavlenskiĭ, O. I. "THE LAX REPRESENTATION WITH A SPECTRAL PARAMETER FOR CERTAIN DYNAMICAL SYSTEMS." Mathematics of the USSR-Izvestiya 32, no. 2 (1989): 245–68. http://dx.doi.org/10.1070/im1989v032n02abeh000757.

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46

Polgárdi, Krisztina. "The representation of lax vowels in Dutch: A loose CV approach." Lingua 118, no. 9 (2008): 1375–92. http://dx.doi.org/10.1016/j.lingua.2007.09.008.

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47

Bruschi, M., and F. Calogero. "The Lax representation for an integrable class of relativistic dynamical systems." Communications in Mathematical Physics 109, no. 3 (1987): 481–92. http://dx.doi.org/10.1007/bf01206147.

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48

Irfan, M. "Lax pair representation and Darboux transformation of noncommutative Painlevé’s second equation." Journal of Geometry and Physics 62, no. 7 (2012): 1575–82. http://dx.doi.org/10.1016/j.geomphys.2012.01.008.

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49

Strauss, Y., L. P. Horwitz, and E. Eisenberg. "Representation of quantum mechanical resonances in the Lax–Phillips Hilbert space." Journal of Mathematical Physics 41, no. 12 (2000): 8050–71. http://dx.doi.org/10.1063/1.1310359.

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50

Adler, M., T. Shiota, and P. van Moerbeke. "A Lax representation for the vertex operator and the central extension." Communications in Mathematical Physics 171, no. 3 (1995): 547–88. http://dx.doi.org/10.1007/bf02104678.

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