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Journal of Nonlinear Mathematical Physics Volume 9, 2002 - Issue sup1: Recent Advances in Integrable Systems
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Original Articles

A List of 1+1 Dimensional Integrable Equations and Their Properties

Jing Ping Wang Division of Mathematics & Computer Science, Faculty of Sciences, Vrije Universiteit, Amsterdam, The Netherlands E-mail: [email protected]
Pages 213-233 | Received 29 Aug 2001, Accepted 01 Nov 2001, Published online: 21 Jan 2013

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M.E. Fels & E. Yaşar. (2019) Variational Operators, Symplectic Operators, and the Cohomology of Scalar Evolution Equations. Journal of Nonlinear Mathematical Physics 26:4, pages 604-649.
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Stephen C. Anco, Shahid Mohammad, Thomas Wolf & Chunrong Zhu. (2016) Generalized negative flows in hierarchies of integrable evolution equations. Journal of Nonlinear Mathematical Physics 23:4, pages 573-606.
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D. E. Baldwin & W. Hereman. (2010) A symbolic algorithm for computing recursion operators of nonlinear partial differential equations. International Journal of Computer Mathematics 87:5, pages 1094-1119.
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Articles from other publishers (53)

Bao Wang. (2023) Generalized conditional symmetries and pre-Hamiltonian operators. Journal of Mathematical Physics 64:9.
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M. Casati, P. Lorenzoni, D. Valeri & R. Vitolo. (2022) Weakly nonlocal Poisson brackets: Tools, examples, computations. Computer Physics Communications 274, pages 108284.
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Annalisa Calini & Thomas Ivey. (2021) Integrable geometric flows for curves in pseudoconformal S3. Journal of Geometry and Physics 166, pages 104249.
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Matteo Casati, Paolo Lorenzoni & Raffaele Vitolo. (2020) Three computational approaches to weakly nonlocal Poisson brackets. Studies in Applied Mathematics 144:4, pages 412-448.
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P. Lorenzoni & R. Vitolo. (2020) Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds. Journal of Geometry and Physics 149, pages 103573.
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Marianna Euler & Norbert Euler. (2019) On Möbius‐invariant and symmetry‐integrable evolution equations and the Schwarzian derivative. Studies in Applied Mathematics 143:2, pages 139-156.
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Hernán A. González, Javier Matulich, Miguel Pino & Ricardo Troncoso. (2018) Revisiting the asymptotic dynamics of General Relativity on AdS3. Journal of High Energy Physics 2018:12.
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Sandra Carillo. (2018) KdV-type equations linked via Bäcklund transformations: Remarks and perspectives. Applied Numerical Mathematics.
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Mei-Dan Chen & Biao Li. (2018) Classification and Recursion Operators of Dark Burgers’ Equation. Zeitschrift für Naturforschung A 73:2, pages 175-180.
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Kai Tian & Jing Ping Wang. (2017) Symbolic Representation and Classification of N=1 Supersymmetric Evolutionary Equations. Studies in Applied Mathematics 138:4, pages 467-498.
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Sylvain Carpentier. (2017) A sufficient condition for a rational differential operator to generate an integrable system. Japanese Journal of Mathematics 12:1, pages 33-89.
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Anass Bouisaghouane & Arthemy V Kiselev. (2017) Do the Kontsevich tetrahedral flows preserve or destroy the space of Poisson bi-vectors?. Journal of Physics: Conference Series 804, pages 012008.
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Joseph Krasil'shchik, Alexander Verbovetsky & Raffaele VitoloJoseph Krasil’shchik, Alexander Verbovetsky & Raffaele Vitolo. 2017. The Symbolic Computation of Integrability Structures for Partial Differential Equations. The Symbolic Computation of Integrability Structures for Partial Differential Equations 149 168 .
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Xiu-Rong Guo. (2016) Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations. Communications in Theoretical Physics 65:6, pages 735-742.
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A M Wazwaz. (2015) A variety of (3+1)-dimensional KdV equations derived by using the KdV recursion operator. Indian Journal of Physics 90:5, pages 577-582.
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Kai Tian & Q P Liu. (2016) Conservation laws and symmetries of Hunter–Saxton equation: revisited. Nonlinearity 29:3, pages 737-755.
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Guizhang Tu. (2015) An inversion formula for recursion operator of KP hierarchy. Journal of Mathematical Physics 56:12.
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Abdul-Majid Wazwaz. (2015) A variety of (3 + 1)-dimensional Burgers equations derived by using the Burgers recursion operator. Mathematical Methods in the Applied Sciences 38:12, pages 2642-2649.
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Abdul-Majid Wazwaz. (2014) A variety of (3+1)-dimensional mKdV equations derived by using the mKdV recursion operator. Computers & Fluids 93, pages 41-45.
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Oleg Morozov. (2014) A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence. Open Mathematics 12:2.
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Qiusheng CHENG & Jingsong HE. (2014) The Prolongation Structures and Nonlocal Symmetries for Modified Boussinesq System. Acta Mathematica Scientia 34:1, pages 215-227.
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F. Khanizadeh, A. V. Mikhailov & Jing Ping Wang. (2014) Darboux transformations and recursion operators for differential-difference equations. Theoretical and Mathematical Physics 177:3, pages 1606-1654.
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J. H. P. Dawes & H. Susanto. (2013) Variational approximation and the use of collective coordinates. Physical Review E 87:6.
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Abdul-Majid Wazwaz. (2013) (2+1)-Dimensional Burgers equations BE(m+n+1): Using the recursion operator. Applied Mathematics and Computation 219:17, pages 9057-9068.
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Ф Ханизаде, Farbod Khanizadeh, Александр Васильевич Михайлов, Alexander Vasil'evich Mikhailov, Дж П Ванг & Jing Ping Wang. (2013) Преобразования Дарбу и рекурсионные операторы для дифференциально-разностных уравненийDarboux transformations and recursion operators for differential - difference equations. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 177:3, pages 387-440.
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Fu Zhang, Jian-ming Qi & Wen-jun Yuan. (2013) Further Results about Traveling Wave Exact Solutions of the Drinfeld-Sokolov Equations. Journal of Applied Mathematics 2013, pages 1-6.
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Abdul-Majid Wazwaz. (2012) (2+1)-Dimensional mKdV (N) equations by the mKdV recursion operator: Multiple soliton and multiple singular soliton solutions. Applied Mathematics and Computation 219:5, pages 2535-2544.
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M Marvan & A Sergyeyev. (2012) Recursion operators for dispersionless integrable systems in any dimension. Inverse Problems 28:2, pages 025011.
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J. F. Alzaidy. (2012) Extended Mapping Method and Its Applications to Nonlinear Evolution Equations. Journal of Applied Mathematics 2012, pages 1-14.
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A.V. Mikhailov & J.P. Wang. (2011) A new recursion operator for Adlerʼs equation in the Viallet form. Physics Letters A 375:45, pages 3960-3963.
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Petr Vojčák. (2011) On complete integrability of the Mikhailov–Novikov–Wang system. Journal of Mathematical Physics 52:4.
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Kelei Zhang, Shengqiang Tang & Zhaojuan Wang. (2010) Bifurcations of travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov () system. Applied Mathematics and Computation 217:4, pages 1620-1631.
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Deng-Shan Wang. (2010) Integrability of the coupled KdV equations derived from two-layer fluids: Prolongation structures and Miura transformations. Nonlinear Analysis: Theory, Methods & Applications 73:1, pages 270-281.
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Xijun Deng, Jinlong Cao & Xi Li. (2010) Travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov ( ) system . Communications in Nonlinear Science and Numerical Simulation 15:2, pages 281-290.
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G. Chavchanidze. (2009) Non-Noether symmetries of the modified Boussinesq equations. Journal of Mathematical Sciences 160:6, pages 693-696.
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Jing Ping Wang. (2009) Lenard scheme for two-dimensional periodic Volterra chain. Journal of Mathematical Physics 50:2.
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Fuding Xie & Zhenya Yan. (2009) New exact solution profiles of the nonlinear dispersion Drinfel’d–Sokolov (D(m,n)) system. Chaos, Solitons & Fractals 39:2, pages 866-872.
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Huiqun Zhang. (2008) New exact travelling wave solutions to the complex coupled KdV equations and modified KdV equation. Communications in Nonlinear Science and Numerical Simulation 13:9, pages 1776-1781.
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Ren Wen-Xiu & Alatancang. (2007) Bi-Hamiltonian Structure of a Third-Order Nonlinear Evolution Equation on Plane Curve Motions. Communications in Theoretical Physics 48:2, pages 211-214.
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Elizabeth L. Mansfield & Peter H. van der Kamp. (2006) Evolution of curvature invariants and lifting integrability. Journal of Geometry and Physics 56:8, pages 1294-1325.
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Abdul-Majid Wazwaz. (2006) Exact and explicit travelling wave solutions for the nonlinear Drinfeld–Sokolov system. Communications in Nonlinear Science and Numerical Simulation 11:3, pages 311-325.
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Abdul-Majid Wazwaz. (2006) A variety of exact wave solutions with distinct physical structures for the Boussinesq system. Communications in Nonlinear Science and Numerical Simulation 11:3, pages 376-390.
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M.L. Gandarias & S. Saez. (2006) On the Calogero–Degasperis–Fokas equation in dimensions. Physica A: Statistical Mechanics and its Applications 362:2, pages 261-276.
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. 2006. The Mathematica GuideBook for Symbolics. The Mathematica GuideBook for Symbolics 978 1429 .
Partha Guha. (2005) Geodesic flows, bi-Hamiltonian structure and coupled KdV type systems. Journal of Mathematical Analysis and Applications 310:1, pages 45-56.
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George Chavchanidze. (2005) Involutive orbits of non-Noether symmetry groups. Journal of Physics A: Mathematical and General 38:29, pages 6517-6524.
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M. Mariani & F. Calogero. (2005) Isochronous PDEs. Physics of Atomic Nuclei 68:5, pages 899-908.
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A.-M. Wazwaz. (2005) The tanh and the sine-cosine methods for the complex modified K dV and the generalized K dV equations. Computers & Mathematics with Applications 49:7-8, pages 1101-1112.
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A Sergyeyev. (2005) Why nonlocal recursion operators produce local symmetries: new results and applications. Journal of Physics A: Mathematical and General 38:15, pages 3397-3407.
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Niclas Petersson, Norbert Euler & Marianna Euler. (2003) Recursion Operators for a Class of Integrable Third‐Order Evolution Equations. Studies in Applied Mathematics 112:2, pages 201-225.
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J Ram rez, M S Bruz n, C Muriel & M L Gandarias. (2003) The Schwarzian Korteweg de Vries equation in (2   1) dimensions. Journal of Physics A: Mathematical and General 36:5, pages 1467-1484.
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M Marvan & A Sergyeyev. (2003) Recursion operator for the stationary Nizhnik Veselov Novikov equation. Journal of Physics A: Mathematical and General 36:5, pages L87-L92.
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