Related papers: Long Wave Dynamics along a Convex Bottom
In this paper, persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory. Two different kinds of the perturbations are considered in…
We show that in the linear approximation there are three classes of reflectionless wave propagation on a surface of shallow water in the channel with spatially varying depth, width, and current speed. Two of these classes have been…
We study the existence of monotone traveling wave solutions in a class of nonclassical diffusion equations that include both standard diffusion and a higher-order mixed space-time dispersive term. The reaction term is nonlinear and subject…
We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built upon the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two…
Numerical simulations of the unidirectional random waves are performed within the Korteweg -de Vries equation to investigate the statistical properties of surface gravity waves in shallow water. Nonlinear evolution shows the relaxation of…
In this manuscript we perform an extensive numerical study of the long wave interaction problem with a fixed partially immersed body into a fluid layer. The incident wave is assumed to be an isolated solitary wave. The body in this study is…
This paper describes the results from a numerical estimation of the force exerted by long surface waves on a fixed and partially immersed rectangular structure. The topic is connected with the need of making decisions on the design,…
In this note we look at the influence of a shallow, uneven riverbed on a soliton. The idea consists in approximate transformation of the equation governing wave motion over uneven bottom to equation for flat one for which the exact solution…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
In this paper, the large time behavior of solutions of 1-D isentropic Navier-Stokes system is investigated. It is shown that a composite wave consisting of two viscous shock waves is stable for the Cauchy problem provided that the two waves…
We construct a family of explicit rotational solutions to the nonlinear governing equations for water waves, describing edge waves propagating over a plane-sloping beach. A detailed analysis of the edge wave dynamics and of the run-up…
Debris flows often exhibit coherent wave structures-shock-like roll waves on steeper slopes and weaker, more sinusoidal dispersive pulses on gentler slopes. Coarse-rich heads raise basal resistance, whereas fines-rich tails lower it; in…
Dispersive effects during long wave run-up on a plane beach are studied. We take an advantage of experimental data collection of different wave types (single pulses, sinusoidal waves, bi-harmonic waves, and frequency modulated wave trains)…
For a one-dimensional mildly quasilinear wave equation given in the upper half-plane, we consider the Cauchy problem. The initial conditions have discontinuity of the first kind at one point. We construct the solution using the method of…
The two-dimensional propagation of small-amplitude waves through an infinite periodic array of freely-floating rectangular floes is considered under the assumptions of inviscid linearised wave theory. Fluid gaps between adjacent floes allow…
The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time dependent solutions, we simplify the full potential…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
Six-wave interactions are used for modeling various physical systems, including in optical wave turbulence [16] (where a cascade of photons displays this kind of behavior) and in quantum wave turbulence [31] (for the interaction of Kelvin…