Breaking waves and persistence property for a two-component Camassa–Holm system

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

In this paper, we consider two types of solutions of the rotation-two-component Camassa-Holm (R2CH) system, a model in the equatorial water waves with the effect of the Coriolis force. The first type of solutions exhibits finite time singularity in the sense of wave-breaking. We perform a refined analysis based on the local structure of the dynamics to provide some criteria that leads to the bl...

A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS

In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...

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...

Rogue waves in a two-component Manakov system with variable coefficients and an external potential.

We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system may be realized in nonlinear optics and Bose-Einstein condensates. By means of a similarity transformation, we establish a connection between solutions of th...

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