Waves of maximal height for a class of nonlocal equations with inhomogeneous symbols

Article type: Research Article

Authors: Le, Hung^{; *}

Affiliations: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway. E-mail: hung.le@ntnu.no

Correspondence: [*] Corresponding author. E-mail: hung.le@ntnu.no.

Abstract: In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order α for α>1. Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, 2π-periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz.

Keywords: Whitham type, inhomogeneous, nonlocal, maximal height, water waves

DOI: 10.3233/ASY-211694

Journal: Asymptotic Analysis, vol. 127, no. 4, pp. 355-380, 2022