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

Abstract

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

22 pages. arXiv admin note: text overlap with arXiv:1810.00248 by other authors

References in corpus (2)

• Global bifurcation of solitary waves for the Whitham equation
• Enhanced existence time of solutions to evolution equations of Whitham type