Simply-periodic Lamé functions ($\nu $ noninteger) can be used to solve boundary-value problems for Laplace’s equation in elliptical cones. For applications in antenna research see Jansen (1977). Brack et al. (2001) shows that Lamé functions occur at bifurcations in chaotic Hamiltonian systems. Bronski et al. (2001) uses Lamé functions in the theory of Bose–Einstein condensates.

Ward (1987) computes finite-gap potentials associated with the periodic Korteweg–de Vries equation. Shail (1978) treats applications to solutions of elliptic crack and punch problems. Hargrave (1978) studies high frequency solutions of the delta wing equation. Macfadyen and Winternitz (1971) finds expansions for the two-body relativistic scattering amplitudes. Roper (1951) solves the linearized supersonic flow equations. Clarkson (1991) solves nonlinear evolution equations. Strutt (1932) describes various applications and provides an extensive list of references.

See also §29.12(iii).