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Analytic solutions for calcium ion fertilisation waves on the surface of eggs.

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journal contribution
posted on 14.01.2021, 05:57 by Bronwyn H Bradshaw-Hajek, Philip BroadbridgePhilip Broadbridge
© The Author(s) 2019. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. The evolution of calcium fertilisation waves on the cortex of amphibian eggs can be described by a nonlinear reaction-diffusion process on the surface of a sphere. Here, we use the nonclassical symmetry technique to find an exact analytic solution that describes the evolution of the calcium concentration. The solutions presented compare well with published experimental results. The analytic solution can be used to give insight into the processes governing the fertilisation wave, such as the flow of calcium ions from the sperm entry point. By finding a spiral solution to an approximate equation linearised near saturation, we also demonstrate how solutions with other properties may be constructed using this technique.


Publication Date



Mathematical Medicine and Biology: A Journal of the IMA






14p. (p. 549-562)





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