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 …

Peakons are special weak solutions of a class of nonlinear partial differential equations
modelling non-linear phenomena such as the breakdown of regularity and the onset of …

Peakon traveling wave solutions, both on the line and on the circle, are derived for a novel $
ab $-family of nonlocal evolution equations with cubic nonlinearities. At least two members …

Recent generalizations of the Camassa–Holm equation are studied from the point of view of
existence of global solutions, criteria for wave breaking phenomena and integrability. We …

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 …

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 …

In this Letter we propose that for Lax integrable nonlinear partial differential equations the
natural concept of weak solutions is implied by the compatibility condition for the respective …

This paper proposes a higher-order μ-Camassa–Holm equation, which is regarded as a
higher-order extension of the μ-Camassa–Holm equation, and preserves some properties of …

In this paper, we investigate the N− abc family of Camassa–Holm type equation with (N+ 1)-
order nonlinearities. This quasi-linear equation is nonlocal with higher order nonlinearities …

In this paper, we consider the Cauchy problem for the N− abc family of the Camassa–Holm
type equation with both dissipation and dispersion. First, we establish the global well …