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Comment on “Classification of Lie point symmetries for quadratic Liénard type equation \(\ddot{x} + f(x) \dot{x}^2 + g(x) = 0\)”. (English) Zbl 1337.34041

Summary: We demonstrate a simplification of some recent works on the classification of the Lie symmetries for a quadratic equation of Liénard type [A. K. Tiwari et al., ibid. 54, No. 5, 053506, 19 p. (2013; Zbl 1295.34049); ibid. 55, No. 5, 059901, 2 p. (2014; Zbl 1318.34052)]. We observe that the problem could have been resolved more simply.
©2016 American Institute of Physics

MSC:

34C14 Symmetries, invariants of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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References:

[1] Tiwari, A. K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M., J. Math. Phys., 54, 053506 (2013) · Zbl 1295.34049 · doi:10.1063/1.4803455
[2] Tiwari, A. K.; Pandey, S. N.; Senthilvelan, M.; Lakshmanan, M., J. Math. Phys., 55, 059901 (2014) · Zbl 1318.34052 · doi:10.1063/1.4871778
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