We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely).

Recent studies of the evolution of weakly nonlinear long waves in shear flows have revealed that when the wave field contains a critical layer, a new nonlinear wave equation is needed to describe the wave evolution. This equation is of the same type as the well-known Korteweg-de Vries equation but has a more complicated nonlinear structure. Our main interest is in the steady solitary wave solut...

Both theoretical investigations and successful experimental research were performed recently, confirming the existence and demonstrating the main properties of bulk strain solitary waves in nonlinearly elastic solid wave guides. Our current research is devoted to non-linear wave processes in layered elastic wave guides with inhomogeneities modelling damage/delamination. Here, we present first e...

A high resolution modeling study is undertaken, with a 2.5-dimensional nonhydrostatic model, of the generation of internal waves induced by tidal motion over the ridges in Luzon Strait. The model is forced by the barotropic tidal components K1, M2, and O1. These tidal components, along with the initial density field, were extracted from data and models. As the barotropic tide moves over the Luz...

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Ful...

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usuall...

Received October 2, 1992; revised manuscript received December 29, 1992 Separatrices and scaling laws in the switching dynamics of spatial solitary wave pixels are investigated. We show that the dynamics in the full model are similar to those in the plane-wave limit. Switching features may be indicated and explained by the motion of the (complex) solitary wave amplitude in the phase plane. We r...

The interaction of a strongly nonlinear solitary wave with an external force is studied using the extended Korteweg-de Vries equation as a model. This equation has several different families of nonlinear wave solutions: solitons, the so-called ”thick” solitons, algebraic solitons, and breathers, depending upon the sign of the cubic nonlinear term. A simple nonlinear dynamical system of the seco...

We study the stability of the steady waves forced by a moving localised pressure disturbance in water of finite depth. The steady waves take the form of a downstream wavetrain for subcritical flow, but for supercritical flow there is a solution branch for each specified forcing term, which has two localised solitarylike solutions for each Froude number, a small-amplitude and a large-amplitude s...

This article presents a rigorous existence theory for small-amplitude three-dimensional travelling water waves. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable. Wave motions which are periodic in a second, different horizontal direction are detected using a centre-manifold reduction...