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 …

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 …

The boundary value problem for the focusing Kundu–Eckhaus equation with nonzero
boundary conditions is studied by the Dbar dressing method in this work. A Dbar problem …

We investigate the blow-up mechanism of solutions to a class of quasilinear integrable
equations which could possess peakons. The dynamics of the blow-up quantity along the …

In this paper, we are concerned with the finite time blow-up for the high-order Camassa-
Holm-Fokas-Olver-Rosenau-Qiao equations, which is a generalization of the Camassa …

In this paper, we study orbital stability of peakons for the generalized modified Camassa–
Holm (gmCH) equation, which is a natural higher-order generalization of the modified …

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 …

We study the stability of smooth and peaked solitary waves to the modified Camassa-Holm
equation. This quasilinear equation with cubic nonlinearity is completely integrable and …

Abstract The modified Camassa-Holm equation with cubic nonlinearity is completely
integrable and is considered a model for the unidirectional propagation of shallow-water …

In this paper, the formation of singularities for the nonlocal Whitham-type equations is
studied. It is shown that if the lowest slope of flows can be controlled by its highest value with …