Abstract
A geometrical setting for the notion of non-regular additive separation for a PDE, introduced by Kalnins and Miller, is given. This general picture contains as special cases both fixed-energy separation and constrained separation of Helmholtz and Schödinger equations (not necessarily orthogonal). The geometrical approach to non-regular separation allows to explain why it is possible to find some coordinates in Euclidean 3-space where the R-separation of Helmholtz equation occurs, but it depends on a lower number of parameters than in the regular case, and it is apparently not related to the classical Stäckel form of the metric.
The work of the author was supported by Progetto Lagrange of Fondazione CRT and by National Research Project “Geometry of dynamical system”.
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Chanu, C. (2008). Geometry of Non-Regular Separation. In: Eastwood, M., Miller, W. (eds) Symmetries and Overdetermined Systems of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73831-4_14
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DOI: https://doi.org/10.1007/978-0-387-73831-4_14
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