Henrik Kalisch

TL;DR: In this paper, a Hamiltonian perturbation theory for the long wave limits is developed, and a systematic analysis of the principal long wave scaling regimes is carried out, including the Boussinesq and KdV regimes, the Benjamin-Ono regimes, and the intermediate long wave regimes.

TL;DR: The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid as mentioned in this paper.

TL;DR: In this paper, the authors established algebraic lower bounds on the possible rate of decrease in time of the uniform radius of spatial analyticity for generalized Korteweg-de Vries equations.

Abstract: The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves on finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities approach the limiting long-wave speed c0, and the waves approach a solitary wave. It is also shown that there can be no solitary waves with velocities much greater than c0. Finally, numerical approximations of some periodic traveling waves are presented.

TL;DR: In this paper, the authors studied properties of solitary-wave solutions of three evolution equations arising in the modeling of internal waves and found that broad classes of initial data resolve into solitary waves, but also suggest that solitary waves do not interact exactly, thus suggesting two of these equations are not integrable.