The wave breaking for Whitham-type equations revisited

Abstract

We prove wave breaking (shock formation) for some Whitham-type equations which include the Burgers-Hilbert equation, the fractional Korteweg-de Vries equation, and the classical Whitham equation. The result seems to be new for the Burgers-Hilbert equation. In the other cases we provide simpler proofs than the known ones.

References in corpus (3)

• Shock formation for the Burgers-Hilbert equation
• Wave breaking for the Whitham equation with fractional dispersion
• Long time behavior of the fractional Korteweg-de Vries equation with cubic nonlinearity

Cited by in corpus (11)

• Shock formation for the Burgers-Hilbert equation
• On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation
• Enhanced existence time of solutions to evolution equations of Whitham type
• Gradient blow-up for dispersive and dissipative perturbations of the Burgers equation
• Highest Cusped Waves for the Burgers-Hilbert equation
• Wave breaking for the generalized Fornberg-Whitham equation
• On the approximation of vorticity fronts by the Burgers-Hilbert equation
• Refined wave breaking for the generalized Fornberg-Whitham equation
• Stability of traveling waves for the Burgers-Hilbert equation
• Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime
• On the Cauchy problem of dispersive Burgers type equations