Abstract We classify generalized Camassa–Holm-type equations which possess infinite
hierarchies of higher symmetries. We show that the obtained equations can be treated as …

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 this paper, we investigate the formation of singularities and the existence of peaked
traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The …

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> …

A direct and systematic algorithm is proposed to find one-dimensional optimal system for the
group invariant solutions, which is attributed to the classification of its corresponding one …

In this paper, we study the soliton resolution and large time behavior of solutions to the
Cauchy problem for the Novikov equation with a nonzero background ut− utx x+ 4 ux= 3 …

Recently, Novikov found a new integrable equation (we call it the Novikov equation in this
paper), which has nonlinear terms that are cubic, rather than quadratic, and admits peaked …

Considered herein is the dynamical stability of the single peaked soliton and periodic
peaked soliton for an integrable modified Camassa-Holm equation with cubic nonlinearity …

In the paper, we mainly study the existence and uniqueness of global weak solutions for the
Novikov equation. We first recall some results and definitions on strong solutions and weak …

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