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Journal of Nonlinear Mathematical Physics Volume 14, 2007 - Issue 2
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Original Articles

The Riccati and Ermakov-Pinney hierarchies

Marianna Euler Department of Mathematics,, Luleå University of Technology, Luleå, Sweden, SE-971 87 E-mail: [email protected]
,
Norbert Euler Department of Mathematics, Luleå University of Technology, Luleå, Sweden, SE-971 87 E-mail: [email protected]
&
Peter Leach School of Mathematical Sciences, Howard College, University of KwaZulu-Natal, Durban, Republic of South Africa, 4041 E-mail: [email protected]
Pages 290-310 | Published online: 21 Jan 2013

Citations (17)

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P.G.L. Leach & Andronikos Paliathanasis. (2021) A systematic analysis of the properties of the generalised Painlevé-Ince equation. Quaestiones Mathematicae 44:1, pages 1-6.
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Articles from other publishers (16)

Jose M. Cerveró & Pilar G. Estévez. (2021) A Review in Ermakov Systems and Their Symmetries. Symmetry 13:3, pages 493.
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Amlan K. Halder, Andronikos Paliathanasis & P.G.L. Leach. (2019) Singularity analysis of a variant of the Painlevé–Ince equation. Applied Mathematics Letters 98, pages 70-73.
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M. C. Nucci. (2016) Ubiquitous symmetries. Theoretical and Mathematical Physics 188:3, pages 1361-1370.
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R. Gladwin Pradeep, V.K. Chandrasekar, R. Mohanasubha, M. Senthilvelan & M. Lakshmanan. (2016) Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains. Communications in Nonlinear Science and Numerical Simulation 36, pages 303-318.
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М К Нуччи & Maria Clara Nucci. (2016) Вездесущие симметрииUbiquitous symmetries. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 188:3, pages 459-469.
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Oscar Rosas-Ortiz, Octavio Castaños & Dieter Schuch. (2015) New supersymmetry-generated complex potentials with real spectra. Journal of Physics A: Mathematical and Theoretical 48:44, pages 445302.
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Kyriakos Charalambous & Peter Leach. (2015) Properties of the sums of resonances found in the singularity analysis of certain classes of ordinary differential equations. Journal of Physics: Conference Series 621, pages 012003.
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Ajey K. Tiwari, S. N. Pandey, M. Senthilvelan & M. Lakshmanan. (2014) Erratum: “Classification of Lie point symmetries for quadratic Liénard type equation $\ddot{x}+f(x)\dot{x}^2+g(x)=0$ẍ+f(x)ẋ2+g(x)=0” [J. Math. Phys. 54, 053506 (2013)]. Journal of Mathematical Physics 55:5.
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C. Muriel & J.L. Romero. (2014) -symmetries of some chains of ordinary differential equations. Nonlinear Analysis: Real World Applications 16, pages 191-201.
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A. Ghose Choudhury & Partha Guha. (2014) Damped equations of Mathieu type. Applied Mathematics and Computation 229, pages 85-93.
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P. G. L. Leach. (2012) Derivatives of differential sequences. Journal of Engineering Mathematics 82:1, pages 5-16.
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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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J. de Lucas & C. Sardón. (2013) On Lie systems and Kummer-Schwarz equations. Journal of Mathematical Physics 54:3.
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N. Euler & P. G. L. Leach. (2009) Aspects of proper differential sequences of ordinary differential equations. Theoretical and Mathematical Physics 159:1, pages 474-487.
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V.K Chandrasekar, M Senthilvelan & M Lakshmanan. (2008) On the complete integrability and linearization of nonlinear ordinary differential equations. IV. Coupled second-order equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465:2102, pages 609-629.
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P.G.L. Leach. (2008) Symmetry and singularity properties of the generalised Kummer–Schwarz and related equations. Journal of Mathematical Analysis and Applications 348:1, pages 487-493.
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