FURTHER GENERALISATIONS OF THE KUMMER-SCHWARZ EQUATION: ALGEBRAIC AND SINGULARITY PROPERTIES

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

Abstract


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.

Keywords


Kummer-Schwarz; Symmetries; Singularities; Integrability

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague