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 …

This paper is concerned with the modified Camassa–Holm equation and its Bäcklund
transformation. With the aid of reciprocal transformation and the associated modified …

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 …

It is complicated to analyze many events taking place in nature. Idealization which can be
defined as neglecting the nonlinear parts of the event can be used to facilitate a …

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 …

Abstract The Camassa–Holm hierarchy can be regarded as isospectral flows of the
inhomogeneous string. This paper is devoted to the exploration of the second flow in the …

In this paper, a new exact solution of the conformable Gilson–Pickering equation is
investigated. It should be noted that some of the individual cases of the Gilson–Pickering …

In this paper we are concerned with the spectral problem (y 1 y 2) x=(− 1 2 1 2 λ m− 1 2 λ m
1 2)(y 1 y 2) for the periodic generalized Camassa-Holm equations. The first aim is to study …

We study the Lyapunov stability of the periodic generalized Camassa–Holm equation in
terms of the periodic/anti-periodic eigenvalues and the associated spectral intervals …