Related papers: Wave breaking in a shallow water model

We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…

In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation…

We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due…

We prove the local well-posedness for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime.

We determine the stability and instability of a sufficiently small and periodic traveling wave to long wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa-Holm equation to include all the dispersion of…

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…

General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves…

Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wavefunction is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can…

We consider solutions to the linear wave equation on non-compact Riemannian manifolds without boundary when the geodesic flow admits a filamentary hyperbolic trapped set. We obtain a polynomial rate of local energy decay with exponent…

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in…

We consider discrete nonlinear Schr\"odinger equations of n sites with periodic boundary conditions. These equations have n branches of standing waves that bifurcate from zero. Traveling waves appear as a symmetry-breaking from the standing…

This paper is concerned with the detailed behaviour of roll-waves undergoing a low-frequency perturbation. We rst derive the so-called Whitham's averaged modulation equations and relate the well-posedness of this set of equations to the…

We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low…

We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing…

In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak…

Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham…

This study deals with the analysis of the Cauchy problem of a general class of nonlocal nonlinear equations modeling the bi-directional propagation of dispersive waves in various contexts. The nonlocal nature of the problem is reflected by…

In the paper a new nonlinear equation describing shallow water waves with the topography of the bottom directly taken into account is derived. This equation is valid in the weakly nonlinear, dispersive and long wavelength limit. Some…

The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…