Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

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

We consider a family of non-local evolution equations including the 0− Holm-Staley
equation. We show that the family considered does not possess compactly supported …

In this paper we consider a five-parameter equation including the Camassa-Holm and the
Dullin-Gottwald-Holm equations, among others. We prove the existence and uniqueness of …

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 …

In this article, we recover a variety of new families of shallow water wave and solitary wave
solutions to the (1+ 1)-dimensional Dullin “Gottwald” Holm (DGH) system by employing new …

Peaked periodic waves in the Camassa--Holm equation are revisited. Linearized evolution
equations are derived for perturbations to the peaked periodic waves, and linearized …

In this paper, we consider the Cauchy problem for the generalized Camassa–Holm equation
that containing, as its members, three integrable equations: the Camassa–Holm equation …

The bounded traveling wave solutions of a generalized Camassa-Holm-Novikov equation
with p= 2 and p= 3 are derived via the dynamical system approach. The singular wave …

In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm
equation and as a result reduction of the order and computing the conservation laws are …