We study the periodic Cauchy problem for an integrable equation with cubic nonlinearities
introduced by Novikov. Like the Camassa–Holm and Degasperis–Procesi equations …

There is no need for a lengthy summary of the material in this book; a look at the table of
contents should give a first idea of what it is about; details are provided in the introductions …

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 …

We first establish the local well-posedness for the Cauchy problem of the two-component
Euler–Poincaré system in nonhomogeneous Besov spaces. Then, we derive a blow-up …

This work presents an Ovsyannikov type theorem for an autonomous abstract Cauchy
problem in a scale of decreasing Banach spaces, which in addition to existence and …

We show that the solution map of the Camassa-Holm equation is not uniformly continuous in
the initial data in the Sobolev space of order one on the torus and the real line. The proof …

In this paper we mainly investigate the Cauchy problem of some Camassa-Holm type
systems. By constructing a new auxiliary function, we present a generalized Ovsyannikov …

A new nonlinear dispersive partial differential equation with cubic nonlinearity, which
includes the famous Novikov equation as special case, is investigated. We first establish the …

This paper is mainly concerned with the Cauchy problem for a modified two-component
Camassa–Holm shallow water system with analytic initial data. The analyticity of its solutions …

In this paper, we delve into the b-family of equations and explore regularity properties of its
global solutions. Our findings reveal that, irrespective of the real choice of the constitutive …