Breaking Waves And Solitary Waves To The Rotation-Two-Component Camassa-Holm System

Stability Of Solitary Waves Of A Generalized Two-Component Camassa-Holm System

We study here the existence of solitary wave solutions of a generalized twocomponent Camassa-Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped solitary waves. We also demonstrate that all smooth solitary waves are orbitally stable in the energy space. We finally give a sufficient condition for global str...

Global conservative solutions of the Camassa-Holm equation

This paper develops a new approach in the analysis of the Camassa-Holm equation. By introducing a new set of independent and dependent variables, the equation is transformed into a semilinear system, whose solutions are obtained as fixed points of a contractive transformation. These new variables resolve all singularities due to possible wave breaking. Returning to the original variables, we ob...

Stability of Solitary Waves and Global Existence of a Generalized Two-Component Camassa–Holm System

Wave-Breaking and Global Existence for a Generalized Two-Component Camassa-Holm System

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 system also generalizes a class of dispersive waves in cylindrical compressible hyperelastic rods. We show that this new system can still exhibit the wave-breaking phenomenon. We also determine the exact blow-up rate of such...

Global Dissipative Solutions of the Camassa-Holm Equation

This paper is concerned with the global existence of dissipative solutions to the Camassa-Holm equation after wave breaking. By introducing a new set of independent and dependent variables, the evolution problem is rewritten as an O.D.E. in an L∞ space, containing a non-local source term which is discontinuous but has bounded directional variation along a suitable cone of directions. For a give...