Highest Cusped Waves for the Burgers-Hilbert equation

Abstract

In this paper we prove the existence of a periodic highest, cusped, traveling wave solution for the Burgers-Hilbert equation $f_t+f{f}_x=H[f]$ and give its asymptotic behaviour at $0$. The proof combines careful asymptotic analysis and a computer-assisted approach.

44 pages, 3 figures

References in corpus (6)

• Wave breaking for the Whitham equation with fractional dispersion
• Real zeros of 2F1 hypergeometric polynomials
• On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation
• A counterexample to Payne's nodal line conjecture with few holes
• Periodic Hölder waves in a class of negative-order dispersive equations
• On the precise cusped behaviour of extreme solutions to Whitham-type equations

Cited by in corpus (1)

• Smooth imploding solutions for 3D compressible fluids