Related papers: Two-component equations modelling water waves with…

In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…

This paper is concerned with the derivation of a two-component system modelling shallow-water waves with constant vorticity under the Camassa-Holm scaling from our newly established Green-Naghdi equations with a linear shear. It is worth…

Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…

In this paper we apply the approach of formal asymptotic expansions and perturbation theory to derive a new highly nonlinear shallow-water model from the full governing equations for two dimensional incompressible fluid with constant…

For propagation of surface shallow-water waves on irrotational flows, we derive a new two-component system. The system is obtained by a variational approach in the Lagrangian formalism. The system has a non-canonical Hamiltonian…

This article is concerned with the incompressible, infinite depth water wave equation in two space dimensions, with gravity and constant vorticity but with no surface tension. We consider this problem expressed in position-velocity…

Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…

We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation…

In this paper we consider two-dimensional water waves with constant vorticity, under the action of gravity and surface tension, in a fluid domain with finite depth and general bottom topography. We present a formulation which generalizes…

A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of…

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates,and prove that small localized data leads to global…

This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension $d=2$ and in the presence of a fixed partially immersed object. We first show that this…

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 is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates. Viewing this problem as a quasilinear dispersive…

In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Namely, we consider the two-component Camassa-Holm equations,…

We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…