Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): Vera Mikyoung Hur
We prove wave breaking — bounded solutions with unbounded derivatives — in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative, whereby we solve a Whitham's conjecture. We extend the result to equations of Korteweg–de Vries type for a range of fractional dispersion.