R Sinuvasan, K Krishnakumar, K M Tamizhmani, PGL Leach

Further generalisations of the Kummer-Schwarz equation

Číslo: 6/2017
Periodikum: Acta Polytechnica
DOI: 10.14311/AP.2017.57.0467

Klíčová slova: Kummer-Schwarz; Symmetries; Singularities; Integrability, Kummer-Schwarz; Symetrie; Singularita; Integrovanost

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Anotace: The Kummer–Schwarz Equation, 2y'y'''− 3(y'')2 = 0, has a generalisation, (n − 1)y(n−2)y(n) − ny(n−1)2 = 0, which shares many properties with the parent form in terms of symmetry and singularity. All equations of the class are integrable in closed form. Here we introduce a new class, (n+q−2)y(n−2)y(n) −(n+q−1)y(n−1)2 = 0, which has different integrability and singularity properties.