This work studies the initial value problem for a Camassa–Holm type equation with cubic
nonlinearities that has been recently discovered by Vladimir Novikov to be integrable. For s> …

This work studies the initial value problem (ivp) for a generalized Camassa-Holm equation
with (k+1)-order nonlinearities (gk bCH) and containing, as its members, three integrable …

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 …

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 …

The Novikov equation (NE) has been discovered recently as a new integrable equation with
cubic nonlinearities that is similar to the Camassa-Holm and Degasperis-Procesi equations …

We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa–
Holm equations. The smooth solitary waves exist on the constant background. In the …

For s< 3/2, it is shown that the Cauchy problem for the Degasperis-Procesi equation (DP) is
ill-posed in Sobolev spaces H s. If 1/2≤ s< 3/2, then ill-posedness is due to norm inflation …

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 the present work we revisit the b-family model of peakon equations, containing as special
cases the b= 2 (Camassa–Holm) and b= 3 (Degasperis–Procesi) integrable examples. We …

We consider a quasilinear equation that consists of the inviscid Burgers equation plus O (α
2) nonlinear terms. As we show, these extra terms regularize the Burgers equation in the …