References
- M.J. Ablowitz, A. Ramani, and H. Segur, Nonlinear Evolution Equations and Ordinary Differential Equations of Painlevé Type, Lett. Nuovo Cimento 23 (1978), 333–337. doi: 10.1007/BF02824479
- M.J. Ablowitz, A. Ramani, and H. Segur, A connection between nonlinear evolution equations and ordinary differential equations of P type I, J. Math. Phys. 21 (1980), 715–721. doi: 10.1063/1.524491
- M.J. Ablowitz, A. Ramani, and H. Segur, A connection between nonlinear evolution equations and ordinary differential equations of P type II, J. Math. Phys. 21 (1980), 1006–1015. doi: 10.1063/1.524548
- K. Andriopoulos, S. Dimas, P.G.L. Leach, and D. Tsoubelis, On the systematic approach to the classification of differential equations by group theoretical methods, Journal of Computational and Applied Mathematics 230(1) (2009), 224–232. doi: 10.1016/j.cam.2008.11.002
- K. Andriopoulos and P.G.L. Leach, An interpretation of the presence of both positive and negative nongeneric resonances in the singularity analysis, Physics Let- ters A 359 (2006), 199–203.
- K. Andriopoulos, P.G.L. Leach, and A. Maharaj, On Differential Sequences, Applied Mathematics and Information Sciences 5(3) (2011), 484–499.
- S. Dimas, Partial Differential Equations, Algebraic Computing and Nonlinear Sys- tems, Ph.D. Thesis, University of Patras, Greece, 2008.
- S. Dimas and D. Tsoubelis, SYM: A new symmetry-finding package for Mathemat- ica, In: Proceedings of the 10th International Conference in Modern Group Analysis, pp. 64–70, University of Cyprus, Greece, October 2004.
- S. Dimas and D. Tsoubelis, A new Mathematica-based program for solving overdetermined systems of PDEs, In: 8th International Mathematica Symposium, Palais des Papes, Avignon, June 2006.
- M. Euler, N. Euler, and P.G.L. Leach, The Riccati and Ermakov-Pinney hier- archies, Journal of Nonlinear Mathematical Physics 14 (2007), 290–310.
- M. Euler, N. Euler, and P.G.L. Leach, Properties of the Calogero-Degasperis-Ibragimov-Shabat Differ- ential Sequence, Lobachevskii Journal of Mathematics 32 (2011), 61–70.
- N. Euler and P.G.L. Leach, Aspects of proper differential sequences of ordinary differential equations, Theoretical and Mathematical Physics 159 (2009), 473–486. (0040-5779/09/1591-0473)
- N. Euler and P.G.L. Leach, A novel Riccati Sequence, Journal of Nonlinear Mathematical Physics 16(s01) (2009), 157–164.
- M.R. Feix, C. Géronimi, L. Cairó, P.G.L. Leach, R.L. Lemmer, and S.É. Bouquet, On the singularity analysis of ordinary differential equations invariant under time translation and rescaling, Journal of Physics A: Mathematical and General 30 (1997), 7437–7461. doi: 10.1088/0305-4470/30/21/017
- R.L. Lemmer and P.G.L. Leach, The Painlevé test, hidden symmetries and the equation y′′ + yy′3 = 0, J. Phys. A: Math. Gen. 26 (1993), 5017–5024. doi: 10.1088/0305-4470/26/19/030
- F.M. Mahomed and P.G.L. Leach, The linear symmetries of a nonlinear differential equation, Quaestiones Mathematicae 8 (1985), 241–274.
- V.V. Morozov, Classification of six-dimensional nilpotent Lie algebras, Izvestia Vysshikh Uchebn Zavendeniĭ Matematika 5 (1958), 161–171.
- G.M. Mubarakzyanov, On solvable Lie algebras, Izvestia Vysshikh Uchebn Zaven- deniĭ Matematika 32 (1963), 114–123.
- G.M. Mubarakzyanov, Classification of real structures of five-dimensional Lie algebras, Izvestia Vysshikh Uchebn Zavendenĭı Matematika 34 (1963), 99–106.
- G.M. Mubarakzyanov, Classification of solvable six-dimensional Lie algebras with one nilpotent base element, Izvestia Vysshikh Uchebn Zavendenĭı Matematika 35 (1963), 104–116.
- A. Paliathanasis and P.G.L. Leach, Nonlinear Ordinary Differential Equations: A discussion on Symmetries and Singularities, International Journal of Geometric Methods in Modern Physics 13 (2016), 1630009.