Abstract
A method, based on the spatio-temporal focusing phenomenon, is proposed to find the wave trains whose evolution leads to freak wave formation. The model is based on the classical Korteweg–de Vries equation. It is shown on the one hand that the Ursell number which measures nonlinearity with regards to dispersion is weak, that is to say freak waves are quasi-linear, and on the other hand that the phenomenon is a rare event with a short-lived character.
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