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Journal articles on the topic 'Lax pair'

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Published: 4 June 2021

Last updated: 7 July 2024

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1

Juanda, Andreno. "KAJIAN TENTANG LAX PAIR DAN PENERAPANNYA PADA PERSAMAAN LIOUVILLE." Jurnal Matematika UNAND 6, no. 1 (February 1, 2017): 58. http://dx.doi.org/10.25077/jmu.6.1.58-65.2017.

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Abstrak. Lax pair merupakan pasangan dua operator diferensial yang jika disubstitusikanke suatu persamaan (dinamakan persamaan Lax) akan menghasilkan suatu persamaandiferensial parsial tertentu. Jika suatu persamaan diferensial parsial memilikiLax pair, maka hal itu mengindikasikan bahwa persamaan diferensial tersebut bersifatintegrable. Dalam makalah ini akan dibahas analisis Lax pair secara umum, baik dalambentuk operator L dan M maupun dalam bentuk matriks X dan T. Selain itu juga dibahaspenerapan Lax pair secara khusus pada persamaan Liouville dengan mengkonrmasisifat-sifat terkait.Kata Kunci: Persamaan diferensial, Lax pair, Persamaan Liouville

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2

Satria, Ance. "ANALISIS LAX PAIR DAN PENERAPANNYA PADA PERSAMAAN KORTEWEG-DE VRIES." Jurnal Matematika UNAND 6, no. 1 (February 1, 2017): 66. http://dx.doi.org/10.25077/jmu.6.1.66-73.2017.

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Abstrak. Lax pair adalah pasangan dua operator diferensial yang jika disubstitusikanke suatu persamaan (dinamakan persamaan Lax) akan menghasilkan suatu persamaandiferensial parsial tertentu. Pada makalah ini dibahas konsep Lax pair secara umum,baik dalam bentuk operator L dan M maupun dalam bentuk matriks X dan T, serta penerapannya secara khusus pada persamaan Korteweg-de Vries orde lima. Beberapa sifat Lax pair juga dibuktikan, yaitu (i) kuantitas M , dimana suatu fungsi eigen, merupakan solusi dari persamaan L = , dimana suatu nilai eigen, (ii) nilai Trace(Tkt) selalu konstan untuk setiap k 2 N dan (iii) setiap nilai eigen matriks T bernilai konstan.Kata Kunci : Lax pair, operator diferensial, persamaan Lax, persamaan Korteweg-deVries, fungsi eigen, nilai eigen, Trace

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3

BALEANU, D., and S. BAŞKAL. "GEOMETRIZATION OF THE LAX PAIR TENSORS." Modern Physics Letters A 15, no. 24 (August 10, 2000): 1503–10. http://dx.doi.org/10.1142/s0217732300001924.

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The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion tensor. Three-dimensional space–times admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.

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4

Zhang, Yufeng, and Yan Wang. "A New Reduction of the Self-Dual Yang–Mills Equations and its Applications." Zeitschrift für Naturforschung A 71, no. 7 (July 1, 2016): 631–38. http://dx.doi.org/10.1515/zna-2016-0138.

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AbstractThrough imposing on space–time symmetries, a new reduction of the self-dual Yang–Mills equations is obtained for which a Lax pair is established. By a proper exponent transformation, we transform the Lax pair to get a new Lax pair whose compatibility condition gives rise to a set of partial differential equations (PDEs). We solve such PDEs by taking different Lax matrices; we develop a new modified Burgers equation, a generalised type of Kadomtsev–Petviasgvili equation, and the Davey–Stewartson equation, which also generalise some results given by Ablowitz, Chakravarty, Kent, and Newman.

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5

Goliath, Martin, Max Karlovini, and Kjell Rosquist. "Lax pair tensors in arbitrary dimensions." Journal of Physics A: Mathematical and General 32, no. 18 (January 1, 1999): 3377–83. http://dx.doi.org/10.1088/0305-4470/32/18/311.

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6

Yue, Ruihong, and Ryu Sasaki. "Lax Pair forSU(n) Hubbard Model." Journal of the Physical Society of Japan 67, no. 9 (September 15, 1998): 2967–69. http://dx.doi.org/10.1143/jpsj.67.2967.

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7

Estévez, P. G., M. L. Gandarias, and J. Prada. "Symmetry reductions of a Lax pair." Physics Letters A 343, no. 1-3 (August 2005): 40–47. http://dx.doi.org/10.1016/j.physleta.2005.05.089.

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8

Haine, L., and E. Horozov. "A Lax pair for Kowalevski's top." Physica D: Nonlinear Phenomena 29, no. 1-2 (November 1987): 173–80. http://dx.doi.org/10.1016/0167-2789(87)90053-4.

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9

Rosquist, Kjell, and Martin Goliath. "Lax Pair Tensors and Integrable Spacetimes." General Relativity and Gravitation 30, no. 10 (October 1998): 1521–34. http://dx.doi.org/10.1023/a:1018817209424.

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10

Li, Chong, Lin-Jie Shi, Xiao-Li Wang, Na Wang, and Min-Ru Chen. "On generalized Lax equation of the Lax triple of mKP hierarchy." International Journal of Modern Physics A 35, no. 20 (July 2, 2020): 2050099. http://dx.doi.org/10.1142/s0217751x20500992.

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Based on the Lax pair [Formula: see text] of the mKP hierarchy and the operator Nambu 3-bracket, we propose the generalized Lax equation with respect to the Lax triple [Formula: see text]. For different pairs [Formula: see text] in the generalized Lax equation, a generalized hierarchy including the mKP hierarchy is derived.

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11

Lv, Na, Xuegang Yuan, and Jinzhi Wang. "Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/527916.

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With the aid of symbolic computation, we obtain the symmetry transformations of the (2 + 1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation by Lou’s direct method which is based on Lax pairs. Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. In particular, we consider the reductions of the Lax pair completely. As a result, three reduced (1 + 1)-dimensional equations with their new Lax pairs are presented and some group-invariant solutions of the equation are given.

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12

XU, XI-XIANG. "DARBOUX TRANSFORMATION AND EXPLICIT SOLUTIONS FOR A 3-FIELD INTEGRABLE LATTICE SYSTEM WITH THREE ARBITRARY CONSTANTS." International Journal of Modern Physics B 25, no. 19 (July 30, 2011): 2609–19. http://dx.doi.org/10.1142/s0217979211100485.

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A 3-field integrable lattice system with three arbitrary constants and its Lax pair are presented. In virtue of the Lax pair, a Darboux transformation for the 3-field integrable lattice system is obtained, from which the explicit solutions of the 3-field integrable lattice system are given.

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13

Sogo, Kiyoshi. "A Lax–Moser Pair of Euler’s Top." Journal of the Physical Society of Japan 86, no. 9 (September 15, 2017): 095002. http://dx.doi.org/10.7566/jpsj.86.095002.

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14

SASAKI, R. "Universal Lax Pair for Generalised CalogerosMoser Models." Journal of Non-linear Mathematical Physics 8, Supplement (2001): 254. http://dx.doi.org/10.2991/jnmp.2001.8.supplement.44.

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15

Bădiţoiu, Gabriel, and Steven Rosenberg. "Lax Pair Equations and Connes-Kreimer Renormalization." Communications in Mathematical Physics 296, no. 3 (March 14, 2010): 655–80. http://dx.doi.org/10.1007/s00220-010-1034-7.

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16

Friedlander, Susan, and Misha M. Vishik. "Lax pair formulation for the Euler equation." Physics Letters A 148, no. 6-7 (August 1990): 313–19. http://dx.doi.org/10.1016/0375-9601(90)90809-3.

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17

Hay, Mike, Jarmo Hietarinta, Nalini Joshi, and Frank Nijhoff. "A Lax pair for a lattice modified KdV equation, reductions toq-Painlevé equations and associated Lax pairs." Journal of Physics A: Mathematical and Theoretical 40, no. 2 (December 12, 2006): F61—F73. http://dx.doi.org/10.1088/1751-8113/40/2/f02.

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18

Xu, Bo, Pengchao Shi, and Sheng Zhang. "Non-differentiable fractional odd-soliton solutions of local fractional generalized Broer-Kaup system by extending Darboux transformation." Thermal Science 27, Spec. issue 1 (2023): 77–86. http://dx.doi.org/10.2298/tsci23s1077x.

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In this paper, a local fractional generalized Broer-Kaup (gBK) system is first de?rived from the linear matrix problem equipped with local space and time fractional partial derivatives, i.e, fractional Lax pair. Based on the derived fractional Lax pair, the second kind of fractional Darboux transformation (DT) mapping the old potentials of the local fractional gBK system into new ones is then established. Finally, non-differentiable frcational odd-soliton solutions of the local fractional gBK system are obtained by using two basic solutions of the derived fractional Lax pair and the established fractional DT. This paper shows that the DT can be extended to construct non-differentiable fractional soliton solutions of some local fractional non-linear evolution equations in mathematical physics.

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19

Sakovich, Sergei. "A Note on Lax Pairs of the Sawada-Kotera Equation." Journal of Mathematics 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/906165.

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We prove that the new Lax pair of the Sawada-Kotera equation, discovered recently by Hickman, Hereman, Larue, and Göktaş, and the well-known old Lax pair of this equation, considered in the form of zero-curvature representations, are gauge equivalent to each other if and only if the spectral parameter is nonzero, while for zero spectral parameter a nongauge transformation is required.

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20

Liu, Xue-Ke, and Xiao-Yong Wen. "Continuous Limit, Rational Solutions, and Asymptotic State Analysis for the Generalized Toda Lattice Equation Associated with 3 × 3 Lax Pair." Symmetry 14, no. 5 (April 30, 2022): 920. http://dx.doi.org/10.3390/sym14050920.

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Discrete integrable nonlinear differential difference equations (NDDEs) have various mathematical structures and properties, such as Lax pair, infinitely many conservation laws, Hamiltonian structure, and different kinds of symmetries, including Lie point symmetry, generalized Lie bäcklund symmetry, and master symmetry. Symmetry is one of the very effective methods used to study the exact solutions and integrability of NDDEs. The Toda lattice equation is a famous example of NDDEs, which may be used to simulate the motions of particles in lattices. In this paper, we investigated the generalized Toda lattice equation related to 3×3 matrix linear spectral problem. This discrete equation is related to continuous linear and nonlinear partial differential equations under the continuous limit. Based on the known 3×3 Lax pair of this equation, the discrete generalized (m,3N−m)-fold Darboux transformation was constructed for the first time and extended from the 2×2 Lax pair to the 3×3 Lax pair to give its rational solutions. Furthermore, the limit states of such rational solutions are discussed via the asymptotic analysis technique. Finally, the exponential–rational mixed solutions of the generalized Toda lattice equation are obtained in the form of determinants.

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21

ZHOU, RUGUANG, and ZHENYUN QIN. "AN INTEGRABLE DECOMPOSITION OF THE SYMMETRIC MATRIX KdV EQUATION." Modern Physics Letters B 22, no. 13 (May 30, 2008): 1307–15. http://dx.doi.org/10.1142/s0217984908015383.

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A technique for nonlinearization of the Lax pair for the scalar soliton equations in (1+1) dimensions is applied to the symmetric matrix KdV equation. As a result, a pair of finite-dimensional integrable Hamiltonian systems, which are of higher rank generalization of the classic Gaudin models, are obtained. The integrability of the systems are shown by the explicit Lax representations and r-matrix method.

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22

Krishnaswami, Govind S., and T. R. Vishnu. "The Idea of a Lax Pair-Part II." Resonance 26, no. 2 (February 2021): 257–74. http://dx.doi.org/10.1007/s12045-021-1124-1.

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23

Bernard, Denis, and Nicolas Regnault. "New Lax pair for 2D dimensionally reduced gravity." Journal of Physics A: Mathematical and General 34, no. 11 (March 14, 2001): 2343–52. http://dx.doi.org/10.1088/0305-4470/34/11/325.

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24

Sasaki, R. "Universal Lax Pair for Generalised Calogero–Moser Models." Journal of Nonlinear Mathematical Physics 8, sup1 (January 2001): 254–60. http://dx.doi.org/10.2991/jnmp.2001.8.s.44.

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25

Frolov, Sergey. "Lax pair for strings in Lunin-Maldacena background." Journal of High Energy Physics 2005, no. 05 (May 31, 2005): 069. http://dx.doi.org/10.1088/1126-6708/2005/05/069.

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26

Babelon, O., and M. Talon. "The symplectic structure of rational Lax pair systems." Physics Letters A 257, no. 3-4 (June 1999): 139–44. http://dx.doi.org/10.1016/s0375-9601(99)00298-4.

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27

Krishnaswami, Govind S., and T. R. Vishnu. "The Idea of a Lax Pair—Part I." Resonance 25, no. 12 (December 2020): 1705–20. http://dx.doi.org/10.1007/s12045-020-1091-y.

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28

TINEBRA, FABRIZIO. "THE LAX PAIR OF A GENERALIZED THIRRING MODEL." International Journal of Modern Physics A 14, no. 05 (February 20, 1999): 659–82. http://dx.doi.org/10.1142/s0217751x99000336.

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The system of coupled nonlinear partial differential equations called the Massive Thirring Model is reviewed. In particular it is analyzed in the chiral fermion version, which is extended by introducing a local gauge symmetry in place of the usual global symmetry. This is done by minimally coupling the fermions with a SU L(2) ⊗ SU R(2) gauge potential. Following the formalism of path integrals, we then formulate the study of chiral gauge anomalies in the quantum theory of this gauge extended model. The ultimate goal of it would be to compute the divergence of the chiral fermion current for a nonlinear anomalous theory. Actually, in this work we merely exhibit the Lax pair representation of the system of partial differential equations just derived; it holds to the first order approximation in the infinitesimal gauge parameters and coupling constants present. Our aim is to hint a motivation in searching for explicit solutions of anomalous nonlinear gauge field theories, at least in simple cases.

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29

Zhao, Liu, and Changzheng Qu. "Bosonic super-Liouville system: Lax pair and solution." International Journal of Theoretical Physics 36, no. 7 (July 1997): 1537–46. http://dx.doi.org/10.1007/bf02435754.

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30

Gao, Ya-Jun, Zai-Zhe Zhong, and Yuan-Xing Gui. "Multiple Lax pair for the double Ernst equation." International Journal of Theoretical Physics 36, no. 3 (March 1997): 689–95. http://dx.doi.org/10.1007/bf02435888.

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31

Kimura, Kinji. "A Lax pair of the discrete Euler top." Journal of Physics A: Mathematical and Theoretical 50, no. 24 (May 17, 2017): 245203. http://dx.doi.org/10.1088/1751-8121/aa5df9.

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32

Wadati, Miki, Eugenio Olmedilla, and Yasuhiro Akutsu. "Lax Pair for the One-Dimensional Hubbard Model." Journal of the Physical Society of Japan 56, no. 4 (April 15, 1987): 1340–47. http://dx.doi.org/10.1143/jpsj.56.1340.

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33

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 (November 10, 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 symplectic map and a completely integrable finite-dimensional Hamiltonian system in the Liouville sense. Finally, the involutive representation of solution of the obtained semi-discrete integrable system is presented.

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34

Atchonouglo, K., G. de Saxcé, and M. Ban. "2D ELASTICITY TENSOR INVARIANTS, INVARIANTS DEFINITE POSITIVE CRITERIA." Advances in Mathematics: Scientific Journal 10, no. 8 (August 6, 2021): 2999–3012. http://dx.doi.org/10.37418/amsj.10.8.1.

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In this paper, we constructed relationships with the differents 2D elasticity tensor invariants. Indeed, let ${\bf A}$ be a 2D elasticity tensor. Rotation group action leads to a pair of Lax in linear elasticity. This pair of Lax leads to five independent invariants chosen among six. The definite positive criteria are established with the determined invariants. We believe that this approach finds interesting applications, as in the one of elastic material classification or approaches in orbit space description.

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35

LINA, JEAN-MARC, and PRASANTA K. PANIGRAHI. "LAX PAIR AND COSMOLOGICAL CONSTANT FOR INDUCED 2D-GRAVITY IN THE LIGHT-CONE GAUGE." Modern Physics Letters A 06, no. 38 (December 14, 1991): 3517–24. http://dx.doi.org/10.1142/s0217732391004061.

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We present the Lax pair to describe the two-dimensional induced gravity in the light-cone gauge. This is done at the classical level, with the cosmological constant which so far has not been accounted for in this context. The symmetries are discussed, together with some solutions of the integrability conditions. The case of the W3 gravity is also analyzed; exhibiting some special solutions and highlighting the roles of the two cosmological constants in its Lax pair formulation.

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36

Das, Chandan Kr, and A. Roy Chowdhury. "Complete Integrability Prolongation Structure and Backlund Transformation for the Konno-Onno Equation." Zeitschrift für Naturforschung A 55, no. 5 (May 1, 2000): 545–49. http://dx.doi.org/10.1515/zna-2000-0511.

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Abstract Painleve analysis is used to study the complete integrability of the recently proposed Konno-Onno equation, which also leads to a general form of solutions of the system. An independent study, using the prolongation theory, gives the explicit form of the Lax pair which is then used to obtain the Backlund transformation connecting two sets of solutions of the system. The existence of the Lax pair and the positive result of the Painleve test indicate the complete integrability of the system

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37

Hayashi, Masahito, Kazuyasu Shigemoto, and Takuya Tsukioka. "Two flows Kowalevski top as the full genus two Jacobi’s inversion problem and Sp(4, R ) lie group structure." Journal of Physics Communications 6, no. 2 (February 1, 2022): 025006. http://dx.doi.org/10.1088/2399-6528/ac5161.

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Abstract By using the first and second flows of the Kowalevski top, we can recreate the Kowalevski top into two−flows Kowalevski top, which has two−time variables. Then, we demonstrate that equations of the two−flows Kowalevski top become those of the full genus two Jacobi inversion problem. In addition to the Lax pair for the first flow, we construct a Lax pair for the second flow. Using the first and second flows, we demonstrate that the Lie group structure of these two Lax pairs is Sp(4, R )/ Z 2 ≅ SO ( 3 , 2 ) . With the two−flows Kowalevski top, we can conclude that the Lie group structure of the genus two hyperelliptic function is Sp(4, R )/ Z 2 ≅ SO ( 3 , 2 ) .

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38

Lin, Ji, Xiao-yan Tang, Sen-yue Lou, and Ke-lin Wang. "A New Generalization of the (2+1)-dimensional Davey-Stewartson Equation." Zeitschrift für Naturforschung A 56, no. 9-10 (October 1, 2001): 613–18. http://dx.doi.org/10.1515/zna-2001-0902.

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Abstract Using an asymptotically exact reduction method based on Fourier expansion and spatiotemporal re-scaling, a new integrable system of the nonlinear partial differential equation in (2+1)-dimensions, extended Davey-Stewartson I equation, is deduced from a known (2+1)-dimensional integrable equation. The integrability of the new equation system is explicitly proved by the spectral transformation. Actually, the corresponding Lax pair of the new equations can be obtained by applying the same reduction method to the Lax pair of the original equation.

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39

Liu, De-Yin, Bo Tian, and Xi-Yang Xie. "Bound-state solutions, Lax pair and conservation laws for the coupled higher-order nonlinear Schrödinger equations in the birefringent or two-mode fiber." Modern Physics Letters B 31, no. 12 (April 30, 2017): 1750067. http://dx.doi.org/10.1142/s0217984917500671.

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For describing the propagation of ultrashort pulses in the birefringent or two-mode fiber, we consider the coupled nonlinear Schrödinger equations with higher-order effects. According to the Ablowitz–Kaup–Newell–Segur system, 3[Formula: see text][Formula: see text]3 Lax pair for such equations is derived. Based on the Lax pair, we construct the conservation laws and Darboux transformation (DT). One- and two-soliton solutions are obtained via the DT, and we graphically present the one soliton and bound-state two solitons.

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40

Dzhamay, Anton, and Alisa Knizel. "$q$ -Racah Ensemble and Discrete Painlevé Equation." International Mathematics Research Notices 2020, no. 24 (November 5, 2019): 9797–843. http://dx.doi.org/10.1093/imrn/rnz211.

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Abstract The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlevé equations. Namely, we consider the $q$-Racah polynomial ensemble and show that the one-interval gap probabilities in this case can be expressed through a solution of the discrete $q$-P$\left (E_7^{(1)}/A_{1}^{(1)}\right )$ equation. Our approach also gives a new Lax pair for this equation. This Lax pair has an interesting additional involutive symmetry structure.

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41

LI, LI-LI, BO TIAN, CHUN-YI ZHANG, HAI-QIANG ZHANG, JUAN LI, and TAO XU. "N-SOLITON SOLUTIONS, AUTO-BÄCKLUND TRANSFORMATIONS AND LAX PAIR FOR A NONISOSPECTRAL AND VARIABLE-COEFFICIENT KORTEWEG-DE VRIES EQUATION VIA SYMBOLIC COMPUTATION." International Journal of Modern Physics B 23, no. 10 (April 20, 2009): 2383–93. http://dx.doi.org/10.1142/s0217979209052182.

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In this paper, a nonisospectral and variable-coefficient Korteweg-de Vries equation is investigated based on the ideas of the variable-coefficient balancing-act method and Hirota method. Via symbolic computation, we obtain the analytic N-soliton solutions, variable-coefficient bilinear form, auto-Bäcklund transformations (in both the bilinear form and Lax pair form), Lax pair and nonlinear superposition formula for such an equation in explicit form. Moreover, some figures are plotted to analyze the effects of the variable coefficients on the stabilities and propagation characteristics of the solitonic waves.

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42

Bauyrzhan, G. B., K. R. Yesmakhanova, and K. K. Yerzhanov. "SOLITON GEOMETRY USING THE LAX PAIR OF ISOMONODROMIC DEFORMATION." SERIES PHYSICO-MATHEMATICAL 3, no. 337 (June 12, 2021): 20–25. http://dx.doi.org/10.32014/2021.2518-1726.42.

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43

Hay, Mike. "Lattice modified KdV hierarchy from a Lax pair expansion." Journal of Physics A: Mathematical and Theoretical 46, no. 1 (December 6, 2012): 015203. http://dx.doi.org/10.1088/1751-8113/46/1/015203.

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44

Lima-Santos, A. "Constructing a quantum Lax pair from Yang–Baxter equations." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 05 (May 14, 2009): P05008. http://dx.doi.org/10.1088/1742-5468/2009/05/p05008.

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45

Li, Yanguang (Charles). "A Lax pair for the two dimensional Euler equation." Journal of Mathematical Physics 42, no. 8 (August 2001): 3552–53. http://dx.doi.org/10.1063/1.1378305.

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46

HOU, BO-YU, XIANG-MAO DING, YAN-SHEN WANG, and BO-YUAN HOU. "EXCHANGE RELATIONS OF LAX PAIR FOR NONLINEAR SIGMA MODELS." Modern Physics Letters A 09, no. 17 (June 7, 1994): 1521–28. http://dx.doi.org/10.1142/s0217732394001362.

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We find that the non-ultralocal term s in classical Yang-Baxter r−s matrix consist of Riemann’s connections of target manifold G/H and field-independent projection operators in local coordinates on symmetric space G/H. We give the gauge transformations formula for the Poisson bracket of Lax pair and r−s matrix, and relate these expressions in terms of moving frame with that of fixed frame by current algebra.

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47

Mukherjee, Supriya, and A. Roy Chowdhury. "Lax pair, cyclic basis, and a new integrable system." Chaos, Solitons & Fractals 19, no. 5 (March 2004): 1225–29. http://dx.doi.org/10.1016/s0960-0779(03)00312-6.

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48

Nijhoff, F. W. "Lax pair for the Adler (lattice Krichever–Novikov) system." Physics Letters A 297, no. 1-2 (May 2002): 49–58. http://dx.doi.org/10.1016/s0375-9601(02)00287-6.

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49

Zhou, Ruguang. "Hierarchy of negative order equation and its Lax pair." Journal of Mathematical Physics 36, no. 8 (August 1995): 4220–25. http://dx.doi.org/10.1063/1.530957.

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Bordner, A. J., E. Corrigan, and R. Sasaki. "Generalised Calogero-Moser Models and Universal Lax Pair Operators." Progress of Theoretical Physics 102, no. 3 (September 1, 1999): 499–529. http://dx.doi.org/10.1143/ptp.102.499.

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