Algebraic and Singularity Properties of a Class of Generalisations of the Kummer–Schwarz Equation

Sinuvasan, R.; Tamizhmani, K. M.

doi:10.1007/s12591-016-0327-5

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Cited by 3 publications

(2 citation statements)

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“…where c 1 is the constant of integration. On substitution of equation (19) into equation (18) we have…”

Section: Symmetry Propertiesmentioning

confidence: 99%

Symmetry and Singularity Properties of Steen-Ermakov-Milne-Pinney Equations

Krishnakumar,

Devi,

Sinuvasan

et al. 2019

Preprint

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We examine the general element of the class of ordinary differential equations, yy (n+1) + αy ′ y (n) = 0, for its Lie point symmetries.We observe that the algebraic properties of this class of equations display an attractive set of patterns, the general member of the class can have three type of Algebra, (n + 1)for different values of α. We look at the singularity properties of these equations for various values of α.

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“…where c 1 is the constant of integration. On substitution of equation (19) into equation (18) we have…”

Section: Symmetry Propertiesmentioning

confidence: 99%

Symmetry and Singularity Properties of Steen-Ermakov-Milne-Pinney Equations

Krishnakumar,

Devi,

Sinuvasan

et al. 2019

Preprint

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“…In [12] we delineated the properties of the class of equations (n−1)y (n−2) y (n) −n(y (n−1) ) 2 = 0, n = 2, 3, . .…”

Section: Introductionmentioning

confidence: 99%

Further Generalisations of the Kummer-Schwarz Equation: Algebraic and Singularity Properties

2017

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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 (see Sinuvasan R, Tamizhmani K M & Leach P G L, Algebraic and singularity properties of a class of generalisations of the Kummer-Schwarz equation differ, Equ Dyn Syst (2016), doi:10.1007/s12591-016-0327-5) 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.

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Some properties of the Nesterenko differential sequence

Charalambous

Sinuvasan

2018

Quaestiones Mathematicae

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Algebraic and Singularity Properties of a Class of Generalisations of the Kummer–Schwarz Equation

Cited by 3 publications

References 9 publications

Symmetry and Singularity Properties of Steen-Ermakov-Milne-Pinney Equations

Symmetry and Singularity Properties of Steen-Ermakov-Milne-Pinney Equations

Further Generalisations of the Kummer-Schwarz Equation: Algebraic and Singularity Properties

Some properties of the Nesterenko differential sequence

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