Abstract
A non-linear theory of periodic gravity waves in an incompressible inviscid liquid is presented. The problem which is found to be a singular perturbation problem is treated accordingly with considerable ease. Results for frequency, surface profile and potential function are calculated up to third order as series in powers of a parameter which is the ratio of the amplitude to wavelength. Unlike the linear theory, in this third-order theory, the frequency is found to depend on the amplitude also and decreases with increasing amplitude. The results agree with those obtained earlier by a complicated and labourious method and confirmed by experiments.
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