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 present study several integrable equations with cubic nonlinearity are derived as
asymptotic models from the classical shallow water theory. The starting point in our …

This paper aims at developing the Riemann–Hilbert problem approach to the modified
Camassa–Holm (mCH) equation in the case when the solution is assumed to approach a …

This paper is concerned with the Cauchy problem for a two-component Camassa-Holm
system with high order nonlinearity, which is a multi-component extension of the Fokas …

We study the orbital stability of smooth solitary wave solutions of the Novikov equation,
which is a Camassa–Holm-type equation with cubic nonlinearities. These solitary waves are …

In this paper, we investigate the wave breaking for the Fornberg-Whitham (FW) equation.
Based on blow-up analysis of a Riccati-type inequality with a t-dependent function, which is …

We develop the inverse scattering transform method for the Novikov equation $ u_t-u_ {txx}+
4u^ 2u_x= 3u u_xu_ {xx}+ u^ 2u_ {xxx} $ considered on the line $ x\in (-\infty,\infty) $ in the …

The Novikov equation is a peakon equation with cubic nonlinearity, which, like the Camassa–
Holm and the Degasperis–Procesi, is completely integrable. In this paper, we study the …

It is known from the previous works that the peakon solutions of the Novikov equation are
orbitally and asymptotically stable in $ H^ 1$. We prove, via the method of characteristics …

This paper is concerned with the Cauchy problem for a family of peakon equations with high
order nonlinearity. To begin with, the local well-posedness results in Besov and Sobolev …