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The split-step method is a numerical method that can be used to solve a nonlinear PDE (https://en.wikipedia.org/wiki/Split-step_method). Even Wikipedia does not refer to the original authors (F.D. Tappert and R.H. Hardin in 1974).

The oldest record that I have found (1982) is an old military thesis (Naval Postgraduate School Monterey, CA) that also refers to a paper by Tappert and Hardin on the split-step method. (Link: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=57e1a171c96fc086d2c4e0c05471a3967df7f67e)

Their paper was published in the 8th International Conference on Acoustics (Goldcrest, London, 1974). I have resorted to this link (https://www.icacommission.org/ica-congress/past-ica-proceedings/) but could not find it there.

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  • $\begingroup$ This is just a very particular instance of the more general and older concept known commonly as Lie-Trotter splitting or Godunov splitting (the name depends on which community you ask). It dates back much further than 1974. $\endgroup$
    – David Ketcheson
    Commented Jul 28, 2023 at 18:18
  • $\begingroup$ @DavidKetcheson do you know the original paper that discussed Godunov splitting? $\endgroup$
    – Redsbefall
    Commented Jul 31, 2023 at 11:28
  • $\begingroup$ Is this the paper in question? "R. H. Hardin and F. D. Tappert, Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations, SIAM Review Chronicle, 15:423, 1973" $\endgroup$
    – pluton
    Commented Aug 19, 2023 at 15:41

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The original-original was two talks in 1973 at a Boston SIAM conference, just a descriptive paragraph for each. About a year later there was a more formal talk for Ocean acoustics specialists given by Tappert, proceedings edited by Spofford I think.

For many years citations were to the 1973 talks and then that reference stopped, but that was the original.

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