Wave breaking in a shallow water model
  We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham equation to permit bidirectional wave propagation, provided that the slope of the initial data is sufficiently negative. 
Vera Mikyoung Hur and Lizheng Tao
math.AP