Abstract
A quaternionic partial differential equation is shown to be a generalisation of the traditional Riccati equation and its relationship with the Schrödinger equation is established. Various approaches to the problem of finding particular solutions to this equation are explored, and the generalisations of two theorems of Euler on the Riccati equation, which correspond to this partial differential equation, are stated and proved.
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Kravchenko, V., Kravchenko, V., Williams, B. (2001). A Quaternionic Generalization of the Riccati Differential Equation. In: Brackx, F., Chisholm, J.S.R., Souček, V. (eds) Clifford Analysis and Its Applications. NATO Science Series, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0862-4_14
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DOI: https://doi.org/10.1007/978-94-010-0862-4_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7045-1
Online ISBN: 978-94-010-0862-4
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