In this paper, we study a generalized two-component Camassa–Holm system which can be
derived from the theory of shallow water waves moving over a linear shear flow. This new …

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 …

Considered herein is a two-component Camassa–Holm system modeling shallow water
waves moving over a linear shear flow. It is shown here that solitary-wave solutions of the …

We will discuss a new integrable model which describes the motion of fluid. The present
work is mainly concerned with global existence and blow-up phenomena which are largely …

A new system of equations generalizing the Hunter–Saxton system [Wunsch, Discrete
Contin. Dyn. Syst. Ser. B, 12 (2009), pp. 647–656; Constantin and Ivanov, On an integrable …

ON THE HUNTER–SAXTON SYSTEM Marcus Wunsch 1. Introduction. We introduce the two-component
Hunter–Saxton system of equa- tion Page 1 DISCRETE AND CONTINUOUS doi:10.3934/dcdsb.2009.12.647 …

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 …

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 …

In this paper, we study the wave-breaking phenomena and global existence for the
generalized two-component Hunter–Saxton system in the periodic setting. We first establish …