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 …

An inverse scattering transform method corresponding to a Riemann–Hilbert problem is
formulated for CH2, the two-component generalization of the Camassa–Holm (CH) …

We consider a stochastic Camassa-Holm equation driven by a one-dimensional Wiener
process with a first order differential operator as diffusion coefficient. We prove the existence …

A generalized two‐component model with peakon solutions is proposed in this paper. It
allows an arbitrary function to be involved in as well as including some existing integrable …

In this paper, we develop, analyze and numerically test an invariant-preserving three-level
linearized implicit difference scheme for a rotation-two-component Camassa--Holm system …

We construct a new series of multicomponent integrable PDE systems that contain as
particular example (with appropriately chosen parameters) many famous integrable systems …

A proof that strong solutions of the Dullin–Gottwald–Holm equation vanishing on an open
set of the (1+ 1) space-time are identically zero is presented. In order to do it, we use a …

In this paper, we report an interesting integrable equation that has both solitons and kink
solutions. The integrable equation we study is, which actually comes from the negative KdV …

A new two-component system with cubic nonlinearity and linear dispersion: mt= bux+ 1 2 [m
(uv− uxvx)] x− 1 2 m (uvx− uxv), nt= bvx+ 1 2 [n (uv− uxvx)] x+ 1 2 n (uvx− uxv), m= u− uxx …

A class of multicomponent integrable systems associated with Novikov algebras, which
interpolate between Korteweg–de Vries (KdV) and Camassa–Holm‐type equations, is …