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Non-regular (non-Stäckel) R-separation and general modulated soliton of wave equation

R. Prus·A. Sym
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Abstract

We present a class of orthogonal non-regular in a sense of Kalnins and Miller (hence non-Stäckel) coordinates which are R-separable in 3-dim. Helmholtz equation. One family of parametric surfaces consists of parallel Dupin cyclides, the other two consist of circular cones. This coordinate system is used to simplify derivation of Friedlander's formulae for a general "simple progressive solution of the wave equation" (modulated soliton of wave equation) in $E^3$ and to correct some errors of his paper. The extended version of the paper will be published soon.

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R. Prus, A. Sym. 2004-02-20. Non-regular (non-Stäckel) R-separation and general modulated soliton of wave equation. https://arxiv.org/abs/nlin/0402035

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