History
The full linear dispersion relation was first found by Pierre-Simon Laplace, although there were some errors in his solution for the linear wave problem. The complete theory for linear water waves, including dispersion, was derived by George Biddell Airy and published in about 1840. A similar equation was also found by Philip Kelland at around the same time (but making some mistakes in his derivation of the wave theory).
The shallow water (with small h / λ) limit, ω2 = gh k2, was derived by Joseph Louis Lagrange.
Read more about this topic: Dispersion (water Waves)
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