Wave breaking for a generalized weakly dissipative two-component Camassa–Holm system

Wave-breaking for the Weakly Dissipative Modified Camassa-Holm Equation

The equation (1) arises from an intrinsic (arc-length preserving) invariant planar curve flow in Euclidean geometry and it can be regarded as a Euclidean-invariant version of the Camassa-Holm equation in [1]. It has the form of a modified Camassa-Holm equation with cubic nonlinearity. By Fuchssteiner [2] and Olver and Rosenau[3], it can be derived as a new integrable system by applying the gene...

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...

Weakly-compressible SPH and Experimental modeling of periodic wave breaking on a plane slope

Breaking waves have ability to transport large quantities of sediment and significant impact on coastal structures morphology. Hence, modeling of wave breaking is an important subject in coastal and marine engineering. In this research, the periodic wave breaking process on a plane slope is studied experimentally and numerically. Laboratory experiments were conducted to record water surface ele...

On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

Wave Function Evolution of a Dissipative System

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system...