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Journal of Nonlinear Mathematical Physics Volume 13, 2006 - Issue 4
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Original Articles

Provenance of Type II hidden symmetries from nonlinear partial differential equations

Barbara Abraham-Shrauner Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, 63130, USA E-mail: [email protected]
&
Keshlan S Govinder Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, 4041, Durban, South Africa E-mail: [email protected]
Pages 612-622 | Received 24 Mar 2006, Accepted 28 May 2006, Published online: 21 Jan 2013

Citations (30)

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KESHLAN S. GOVINDER & BARBARA ABRAHAM-SHRAUNER. (2011) ON THE NON-INHERITANCE OF SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS. Journal of Nonlinear Mathematical Physics 18:sup1, pages 135-142.
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M. L. GANDARIAS & M. S. BRUZÓN. (2011) REDUCTIONS FOR SOME ORDINARY DIFFERENTIAL EQUATIONS THROUGH NONLOCAL SYMMETRIES. Journal of Nonlinear Mathematical Physics 18:sup1, pages 123-133.
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GIUSEPPE GAETA. (2009) TWISTED SYMMETRIES OF DIFFERENTIAL EQUATIONS. Journal of Nonlinear Mathematical Physics 16:sup1, pages 107-136.
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Keshlan S Govinder & Barbara Abraham-Shrauner. (2008) On the Origins of Symmetries of Partial Differential Equations: the Example of the Korteweg—de Vries Equation. Journal of Nonlinear Mathematical Physics 15:sup1, pages 60-68.
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Articles from other publishers (26)

R Mohanasubha, V K Chandrasekar, M Senthilvelan & M Lakshmanan. (2023) Finding non-local and contact/dynamical symmetries of Riccati chain. Pramana 97:1.
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J.E. Okeke, R. Narain & K.S. Govinder. (2019) A group theoretic analysis of the generalised Gardner equation with arbitrary order nonlinear terms. Journal of Mathematical Analysis and Applications 479:2, pages 1967-1985.
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M.M. Kassem & A.S. Rashed. (2019) N-solitons and cuspon waves solutions of (2 + 1)-dimensional Broer–Kaup–Kupershmidt equations via hidden symmetries of Lie optimal system. Chinese Journal of Physics 57, pages 90-104.
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Barbara Abraham-Shrauner. (2018) Analytic Solutions of Nonlinear Partial Differential Equations by the Power Index Method. Symmetry 10:3, pages 76.
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Justina Ebele Okeke, Rivendra Narain & Keshlan Sathasiva Govinder. (2018) NEW EXACT SOLUTIONS OF A GENERALISED BOUSSINESQ EQUATION WITH DAMPING TERM AND A SYSTEM OF VARIANT BOUSSINESQ EQUATIONS VIA DOUBLE REDUCTION THEORY. Journal of Applied Analysis & Computation 8:2, pages 471-485.
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Andronikos Paliathanasis & Michael Tsamparlis. (2014) The reduction of the Laplace equation in certain Riemannian spaces and the resulting Type II hidden symmetries. Journal of Geometry and Physics 76, pages 107-123.
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Ben Gao, Zhiyong Zhang & Yufu Chen. (2014) Type-II hidden symmetry and nonlinear self-adjointness of Boiti–Leon–Pempinelli equation. Communications in Nonlinear Science and Numerical Simulation 19:1, pages 29-36.
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Michael Tsamparlis & Andronikos Paliathanasis. (2013) Type II hidden symmetries for the homogeneous heat equation in some general classes of Riemannian spaces. Journal of Geometry and Physics 73, pages 209-221.
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K. Charalambous, C. Sophocleous & P.G.L. Leach. (2013) Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films. Communications in Nonlinear Science and Numerical Simulation 18:8, pages 1949-1958.
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B. Mayil Vaganan. (2012) Cole‐Hopf Transformations for Higher Dimensional Burgers Equations With Variable Coefficients. Studies in Applied Mathematics 129:3, pages 300-308.
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A. Bhuvaneswari, R.A. Kraenkel & M. Senthilvelan. (2012) Application of the -symmetries approach and time independent integral of the modified Emden equation. Nonlinear Analysis: Real World Applications 13:3, pages 1102-1114.
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Alexander Bihlo & Roman O. Popovych. (2012) Lie reduction and exact solutions of vorticity equation on rotating sphere. Physics Letters A 376:14, pages 1179-1184.
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M. S. Bruzon, M. L. Gandarias & M. Senthilvelan. (2012) Nonlocal symmetries of Riccati and Abel chains and their similarity reductions. Journal of Mathematical Physics 53:2.
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P. G. L. Leach, K. S. Govinder & K. Andriopoulos. (2012) Hidden and Not So Hidden Symmetries. Journal of Applied Mathematics 2012, pages 1-11.
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M.S. Bruzon, M.L. Gandarias & M. Senthilvelan. (2011) On the nonlocal symmetries of certain nonlinear oscillators and their general solution. Physics Letters A 375:33, pages 2985-2987.
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You-Ho Lee, Mi-Hye Lee & Jae-Young An. (2011) NEW EXACT TRAVELLING WAVE SOLUTIONS OF SOME NONLIN EAR EVOLUTION EQUATIONS BY THE(G'/G)-EXPANSION METHOD. Honam Mathematical Journal 33:2, pages 247-259.
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Alexander Bihlo & Roman O. Popovych. (2011) Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem. Journal of Mathematical Physics 52:3.
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Maria Luz Gandarias. 2011. Nonlinear Science and Complexity. Nonlinear Science and Complexity 61 66 .
M.L. Gandarias & M.S. Bruzón. (2010) Type II hidden symmetries through weak symmetries for some wave equations. Communications in Nonlinear Science and Numerical Simulation 15:2, pages 291-299.
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Keshlan S. Govinder & Barbara Abraham-Shrauner. (2009) New origins of hidden symmetries for partial differential equations. Nonlinear Analysis: Real World Applications 10:6, pages 3381-3386.
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Alexander Bihlo & Roman O Popovych. (2009) Symmetry Analysis of Barotropic Potential Vorticity Equation. Communications in Theoretical Physics 52:4, pages 697-700.
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M.S. Bruzón & M.L. Gandarias. (2009) Symmetries for a family of Boussinesq equations with nonlinear dispersion. Communications in Nonlinear Science and Numerical Simulation 14:8, pages 3250-3257.
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N.M. Ivanova, R.O. Popovych, C. Sophocleous & O.O. Vaneeva. (2009) Conservation laws and hierarchies of potential symmetries for certain diffusion equations. Physica A: Statistical Mechanics and its Applications 388:4, pages 343-356.
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M.L. Gandarias. (2008) Type-II hidden symmetries through weak symmetries for nonlinear partial differential equations. Journal of Mathematical Analysis and Applications 348:2, pages 752-759.
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Barbara Abraham-Shrauner & Keshlan S. Govinder. (2008) Master partial differential equations for a Type II hidden symmetry. Journal of Mathematical Analysis and Applications 343:1, pages 525-530.
Crossref
Barbara Abraham-Shrauner. (2007) Type II hidden symmetries of the second heavenly equation. Physics Letters A 369:4, pages 299-302.
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