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 ft+ ffx= H[f] , and give its asymptotic behaviour at 0. The proof combines careful asymptotic analysis and a computer-assisted approach. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.