Related papers: Evolution of internal waves in a 2D subcritical ch…

The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave…

Using a matched asymptotic expansion we analyze the two-dimensional, near- critical reflection of a weakly nonlinear, internal gravity wave from a sloping boundary in a uniformly stratified fluid. Taking a distinguished limit in which the…

Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…

We study generation of two-dimensional dispersive shock waves and oblique dark solitons upon interaction of tilted plane waves with negative refractive index defects embedded into defocusing material with linear gain and two-photon…

Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for…

We consider the full 3D dynamics of a thin falling liquid film on a flat plate inclined at some non-zero angle to the horizontal. In addition to gravitational effects, the flow is driven by an electric field, which is normal to the…

Internal waves in a two-layer fluid with rotation are considered within the framework of Helfrich's f-plane extension of the Miyata-Maltseva-Choi-Camassa (MMCC) model. Within the scope of this model, we develop an asymptotic procedure which…

We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…

A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented. The primary surface wave, suitably initiated at some radius, is taken to be a slowly evolving nonlinear cylindrical wave (governed…

Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the…

We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond numbers as fixed and finite, we vary the speed of the…

We study a model of internal waves under periodic forcing in an effectively 2-dimensional aquarium. When the underlying classical dynamics has sufficiently irrational rotation number, we prove that the solution to the internal waves…

We prove the uniform solvability of a stationary problem associated to internal waves equation with small viscosity in a two dimensional aquarium with real-analytic boundary, under a Morse--Smale dynamical assumption. This is achieved by…

We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…

We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…

We consider the linearized instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are not obtained at the highest wave, which has a 120 degree angle at the crest. Under the…

We investigate the evolution of localized initial value profiles when propagated in integrable versions of higher time-derivative theories. In contrast to the standard cases in nonlinear integrable systems, where these profiles evolve into…

We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute…

We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We…