Related papers: On the intermediate long wave propagation for inte…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
Slow flows of an ideal compressible fluid (gas) in the gravity field in the presence of two isentropic layers are considered, with a small difference of specific entropy between them. Assuming irrotational flows in each layer [that is ${\bf…
We present a non-chiral version of the Intermediate Long Wave (ILW) equation that can model nonlinear waves propagating on two opposite edges of a quantum Hall system, taking into account inter-edge interactions. We obtain exact soliton…
We study the small dispersion limit of the intermediate long wave (ILW) equation, specifically on a class of well-behaved initial conditions $u_0$ where the number of solitons in the solution increases without bound. First, we conduct a…
The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…
We study the dynamics of a ferrofluid thin film confined in a Hele-Shaw cell, and subjected to a tilted nonuniform magnetic field. It is shown that the interface between the ferrofluid and an inviscid outer fluid (air) supports traveling…
In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on both the real line and the circle. Our main tool is new…
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
We examine a two-media 2-dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface with wind generated surface waves but considered bounded above by a lid by an assumption…
We consider a density-stratified fluid composed of two immiscible layers separated by a sharp interface. We study the regime of long internal waves interacting with modulated surface wave packets and describe their resonant interaction by a…
This article represents a first step toward understanding the long-time dynamics of solutions for the Intermediate Long Wave equation (ILW). While this problem is known to be both completely integrable and globally well-posed in…
The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…
We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity $s = -\frac 12$ as the critical regularity for ILW with any depth parameter, by…
Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with…
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the…
Variable-coefficient Korteweg - de Vries equation is applied to describe the interfacial wave transformation in two-layer fluid of variable depth. The soliton dynamics in this fluid is studied. The solitary wave breaks in two transient…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant…
The majority of coastal flows are characterized by turbulence, rendering the application of shallow water equations an inadequate approach for their accurate description. This paper presents a theory for characterizing accelerated coastal…