A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov
equations that describe breaking waves is introduced. A classification of low-order …

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 prove well-posedness of the Fornberg–Whitham equation in Besov spaces
B 2, rs in both the periodic and non-periodic cases. This will imply the existence and …

A nonlinear shallow water wave model involving the Fornberg-Whitham equation is
investigated. From the equation itself, we derive several estimates, which are helpful to study …

The subject of this paper is a generalized Camassa–Holm equation under random
perturbation. We first establish local existence and uniqueness results as well as blow-up …

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 …

In this paper, we show that the Fornberg–Whitham equation is Well-posed in Sobolev
spaces H s, for s> 3/2, and in the periodic case. We then show that the Well-posedness is …

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 …

Abstract For s< 3/2 s< 3/2, it is shown that the Cauchy problem for the b-family of equations
is ill-posed in Sobolev spaces H^ s H s on both the torus and the line when b> 1 b> 1. The …

In this paper, the wave breaking of the Fornberg–Whitham equation is studied. We first
investigate the local well-posedness and show a blow-up scenario by local-in-time a priori …