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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

Ghost Symmetries

Peter J Olver School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, U.S.A E-mail: [email protected]
,
Jan A Sanders Vrije Universiteit, Faculty of Sciences, Division of Mathematics, & Computer Science, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands E-mail: [email protected]@cs.vu.nl
&
Jing Ping Wang Vrije Universiteit, Faculty of Sciences, Division of Mathematics, & Computer Science, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands E-mail: [email protected]@cs.vu.nl
Pages 164-172 | Received 07 Jun 2001, Accepted 21 Nov 2001, Published online: 21 Jan 2013

Citations (29)

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P. G.L. Leach & V. Naicker. (2003) Symmetry, Singularity and Integrability: The final question?. Transactions of the Royal Society of South Africa 58:1, pages 1-10.
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M Gürses, A Karasu & R Turhan. (2002) Time-Dependent Recursion Operators and Symmetries. Journal of Nonlinear Mathematical Physics 9:2, pages 210-228.
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Alexander G. Rasin & Jeremy Schiff. (2022) Four Symmetries of the KdV Equation. Journal of Nonlinear Science 32:5.
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Hengchun Hu & Xiaodan Li. (2021) New interaction solutions of the similarity reduction for the integrable (2+1)-dimensional Boussinesq equation. International Journal of Modern Physics B 36:01.
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Hengchun Hu & Xiaodan Li. (2022) Nonlocal symmetry and interaction solutions for the new (3+1)-dimensional integrable Boussinesq equation. Mathematical Modelling of Natural Phenomena 17, pages 2.
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Hengchun Hu & Zhenya Zhang. (2020) Symmetry reduction and new interaction solutions for the negative-order potential KdV equation. Modern Physics Letters B 35:06, pages 2150108.
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Jun Cai Pu & Yong Chen. (2020) Nonlocal symmetries, Bäcklund transformation and interaction solutions for the integrable Boussinesq equation. Modern Physics Letters B 34:26, pages 2050288.
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Lu Zhao & Changzheng Qu. (2020) Nonlocal Symmetries of the Camassa-Holm Type Equations. Chinese Annals of Mathematics, Series B 41:3, pages 407-418.
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Homero G. Díaz-Marín. (2019) A Poisson Algebra for Abelian Yang-Mills Fields on Riemannian Manifolds with Boundary. Symmetry 11:7, pages 880.
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Leonidas Karpathopoulos, Michael Tsamparlis & Andronikos Paliathanasis. (2018) Quadratic conservation laws and collineations: A discussion. Journal of Geometry and Physics 133, pages 279-286.
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A. Sergyeyev. (2017) New integrable ( $$3+1$$ 3 + 1 )-dimensional systems and contact geometry. Letters in Mathematical Physics 108:2, pages 359-376.
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Yueyue Li & Hengchun Hu. (2018) Nonlocal symmetries and interaction solutions of the Benjamin–Ono equation. Applied Mathematics Letters 75, pages 18-23.
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M.B. Sheftel, D. Yazıcı & A.A. Malykh. (2017) Recursion operators and bi-Hamiltonian structure of the general heavenly equation. Journal of Geometry and Physics 116, pages 124-139.
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Jing Kang, Xiaochuan Liu, Peter J. Olver & Changzheng Qu. (2015) Liouville Correspondence Between the Modified KdV Hierarchy and Its Dual Integrable Hierarchy. Journal of Nonlinear Science 26:1, pages 141-170.
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J. P. Wang. (2015) Representations of sl(2, ℂ) in category O and master symmetries. Theoretical and Mathematical Physics 184:2, pages 1078-1105.
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Bo Ren, Xi-Zhong Liu & Ping Liu. (2015) Nonlocal Symmetry Reductions, CTE Method and Exact Solutions for Higher-Order KdV Equation. Communications in Theoretical Physics 63:2, pages 125-128.
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Дж П Ванг & Jing Ping Wang. (2015) Представления алгебры $\mathfrak{sl}(2,\mathbb{C})$ в категории $\mathcal O$ и мастер-симметрииRepresentations of $\mathfrak{sl}(2,\mathbb{C})$ in category $\mathcal O$ and master symmetries. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 184:2, pages 212-243.
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RAFAEL HERNÁNDEZ HEREDERO & ENRIQUE G. REYES. (2013) NONLOCAL SYMMETRIES, COMPACTON EQUATIONS, AND INTEGRABILITY. International Journal of Geometric Methods in Modern Physics 10:09, pages 1350046.
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Rafael Hernández Heredero & Enrique G. Reyes. (2012) Geometric Integrability of the Camassa–Holm Equation. II. International Mathematics Research Notices 2012:13, pages 3089-3125.
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Joseph Krasil’shchik & Alexander Verbovetsky. (2011) Geometry of jet spaces and integrable systems. Journal of Geometry and Physics 61:9, pages 1633-1674.
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Rafael Hernández-Heredero & Enrique G Reyes. (2009) Nonlocal symmetries and a Darboux transformation for the Camassa–Holm equation. Journal of Physics A: Mathematical and Theoretical 42:18, pages 182002.
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V. A. Golovko, I. S. Krasil’shchik & A. M. Verbovetsky. (2008) Variational Poisson-Nijenhuis structures for partial differential equations. Theoretical and Mathematical Physics 154:2, pages 227-239.
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Валентина Александровна Головко, Valentina Aleksandrovna Golovko, Иосиф Семенович Красильщик, Iosif Semenovich Krasil'shchik, Александр Моисеевич Вербовецкий & Alexander Moiseevich Verbovetsky. (2008) Вариационные структуры Пуассона - Нийенхейса на дифференциальных уравнениях в частных производныхVariational Poisson - Nijenhuis structures for partial differential equations. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 154:2, pages 268-282.
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ENRIQUE G. REYES & GUILLERMO SANCHEZ. (2011) EXPLICIT SOLUTIONS TO THE KAUP–KUPERSHMIDT EQUATION VIA NONLOCAL SYMMETRIES. International Journal of Bifurcation and Chaos 17:08, pages 2749-2763.
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Enrique G Reyes. (2007) On nonlocal symmetries of some shallow water equations. Journal of Physics A: Mathematical and Theoretical 40:17, pages 4467-4476.
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Enrique G. Reyes. (2005) Nonlocal symmetries and the Kaup–Kupershmidt equation. Journal of Mathematical Physics 46:7.
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Seyidali S. Akhiev & Teoman Özer. (2005) Symmetry groups of the equations with nonlocal structure and an application for the collisionless Boltzmann equation. International Journal of Engineering Science 43:1-2, pages 121-137.
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Peter J. Olver. 2004. New Trends in Integrability and Partial Solvability. New Trends in Integrability and Partial Solvability 199 215 .
П Темпеста & P Tempesta. (2003) Симметрии Ли и слабая трансверсальностьLie Symmetries and Weak Transversality. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 137:2, pages 293-308.
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