§29.11 Lamé Wave Equation

ⓘ

Keywords:: Lamé wave equation, ellipsoidal wave equation
Permalink:: http://dlmf.nist.gov/29.11
See also:: Annotations for Ch.29

The Lamé (or ellipsoidal) wave equation is given by

29.11.1		$\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+(h-\nu(\nu+1)k^{2}{\operatorname{% sn}}^{2}\left(z,k\right)+k^{2}\omega^{2}{\operatorname{sn}}^{4}\left(z,k\right% ))w=0,$
ⓘ Symbols: $\operatorname{sn}\left(\NVar{z},\NVar{k}\right)$ : Jacobian elliptic function, $\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}$ : derivative of $f$ with respect to $x$ , $z$ : complex variable, $h$ : real parameter, $k$ : real parameter, $\nu$ : real parameter, $\omega$ : parameter and $w(z)$ : solution Referenced by: §29.11, §29.11, §29.18(ii), §29.7(ii) Permalink: http://dlmf.nist.gov/29.11.E1 Encodings: TeX, pMML, png See also: Annotations for §29.11 and Ch.29

in which $\omega$ is another parameter. In the case $\omega=0$ , (29.11.1) reduces to Lamé’s equation (29.2.1).

For properties of the solutions of (29.11.1) see Arscott (1956, 1959), Arscott (1964b, Chapter X), Erdélyi et al. (1955, §16.14), Fedoryuk (1989), and Müller (1966a, b, c).