We study the global well-posedness and wave-breaking phenomenon for the stochastic
rotation-two-component Camassa–Holm (R2CH) system. First, we find a Hamiltonian …

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

In this paper, a modified two-component Camassa–Holm system with the effect of the
Coriolis force in the rotating fluid is derived, which is a model in the equatorial water waves …

We prove existence of a global conservative solution of the Cauchy problem for the two-
component Camassa–Holm (2CH) system on the line, allowing for nonvanishing and distinct …

The Lax pair formulation of the two-component Camassa–Holm equation (CH2) is
generalized to produce an integrable multi-component family, CH (n, k), of equations with n …

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 study here the existence of solitary wave solutions of a generalized two-component
Camassa–Holm system. In addition to those smooth solitary-wave solutions, we show that …

We introduce a novel solution concept, denoted-dissipative solutions are global weak
solutions of the same equation in Eulerian coordinates, yet they exhibit rather distinct …

In this paper, we consider two types of solutions of the rotation-two-component Camassa--
Holm (R2CH) system, a model of equatorial water waves that includes the effect of the …

We study here a generalized two-component integrable Dullin–Gottwald–Holm system,
which can be derived from the Euler equation with constant vorticity in shallow water waves …