In the field of mathematical physics, there exist many physically interesting nonlinear
dispersive equations with peakon solutions, which are solitary waves with discontinuous first …

A general family of peakon equations is introduced, involving two arbitrary functions of the
wave amplitude and the wave gradient. This family contains all of the known breaking wave …

For the Novikov equation, on both the line and the circle, we construct a 2-peakon solution
with an asymmetric antipeakon-peakon initial profile whose H^s-norm for s<3/2 is arbitrarily …

This paper investigates the Cauchy problem for the ab-family of equations with cubic
nonlinearities, which contains the integrable modified Camassa–Holm equation (a= 1 3, b …

The initial value problem for a novel 4-parameter family of evolution equations, which are
nonlinear and nonlocal and possess peakon traveling wave solutions, is studied on both the …

Global analytic solution in both the time and the space variables is proved for the Cauchy
problem of a generalized CH equation, which contains as its members two integrable …

Abstract For the Fokas–Olver–Rosenau–Qiao equation (FORQ), on both the line and the
circle, it is proved that there exist initial data in the Sobolev spaces H s, with s< 3/2, which …

This paper is devoted to understanding how higher-order nonlinearities affect the dispersive
dynamics. As a prototype, a class of higher-order Camassa–Holm equations which can be …

In this paper, we apply a machine-learning approach to learn traveling solitary waves across
various physical systems that are described by families of partial differential equations …

We study the cubic ab-family of equations, which includes both the Fokas-Olver-Rosenau-
Qiao (FORQ) and the Novikov (NE) equations. For a≠ 0, it is proved that there exist initial …