In this paper, we provide a blow-up mechanism to the modified Camassa-Holm equation with varying linear dispersion. We first consider the case when linear dispersion is absent and derive a finite-time blow-up result with an initial data having a region of mild oscillation. A key feature of the analysis is the development of the Burgers-type inequalities with focusing property on characteristics...

The paper presents a sixth-order numerical algorithm for studying the completely integrable CamassHolm (CH) equation. The proposed sixth-order accurate method preserves both the dispersion relation and the Hamiltonians of the CH equation. The CH equation in this study is written as an evolution equation, involving only the first-order spatial derivatives, coupled with the Helmholtz equation. We...

the purpose of this paper is to present a 2d depth-averaged model for simulating and examining unsteady flow patterns in open channel bends. in particular, this paper proposes a 2d depth-averaged model that takes into account the influence of the secondary flow phenomenon through calculation of the dispersion stresses. the dispersion terms which arose from the integration of the product of the ...

The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations.  It can be seen t...

In several problems where a long wavelength oscillatory instability is found, the nonlinear evolution of the perturbations near criticality is governed by the dispersion modified Kuramoto-Sivashinsky equation (KS-KdV). It appears in problems of fluid flow along an inclined plane [ l-31, convection in fluids with a free surface [4], drift waves in plasmas [ 51, vertically falling liquid films in...

In this paper we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schrödinger equation with constant coefficients. This allows us to prove dispersive estimates, which in turn are useful for solving the nonlinear Schrödinger equation. The proof extends also to...