We study the long time asymptotic behavior for the Cauchy problem of the modified
Camassa-Holm (mCH) equation in the solitonic regions m t+(m (u 2− ux 2)) x+ κ ux= 0, m …

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 …

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 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> …

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 …

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 the field of mathematical physics, there exist many physically interesting nonlinear
dispersive equations with peakon solutions, which are solitary waves with discontinuous first …

This paper extracts some analytical solutions of simplified modified Camassa-Holm (SMCH)
equations with various derivative operators, namely conformable and M-truncated …

In this paper, we prove the solution map of the Cauchy problem of Camassa–Holm type
equations depends continuously on the initial data in nonhomogeneous Besov spaces in …