Lie theory and separation of variables. 11. The EPD equation

E. G. Kalnins, Willard Miller

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Abstract

We show that the Euler-Poisson-Darboux equation [∂tt- ∂rr-[(2m+ l)/r]∂r] Θ = 0 separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second-order operators in the enveloping algebra of SL(2, R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second-order operators in the enveloping algebra of SL(2,Cℂ).

Original languageEnglish (US)
Pages (from-to)369-377
Number of pages9
JournalJournal of Mathematical Physics
Volume17
Issue number3
DOIs
StatePublished - 1975
Externally publishedYes

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