Jacobian elliptic functions arise as solutions to certain nonlinear Schrödinger equations, which model many types of wave propagation phenomena. Among these are the formation of vortex rings in Bose Einstein condensates. This image presents the results of a computer simulation of this phenomena carried out at NIST. For details see the NIST news item Decay of a dark soliton into vortex rings in a Bose–Einstein condensate.

For technical details of the physical phenomena, see B.P. Anderson, P.C. Haljan, C.A. Regal, D.L. Feder, L.A. Collins, C.W. Clark, and E.A. Cornell, Watching Dark Solitons Decay into Vortex Rings in a Bose–Einstein Condensate, Phys. Rev. Lett. 86, 2926–2929 (2001)