相关论文: Boussinesq's equations for (2+1)-dimensional gravi…

We study the problem of gravity surface waves for an ideal fluid model in the (2+1)-dimensional case. We apply a systematic procedure to derive the Boussinesq equations for a given relation between the orders of four expansion parameters,…

This article concludes the study of (2+1)-dimensional nonlinear wave equations that can be derived in a model of an ideal fluid with irrotational motion. In the considered case of identical scaling of the $x,y$ variables, obtaining a…

This article is devoted to exact solutions of the Boussinesq equation that models nonlinear shallow water waves. For this we use the Hirota bilinear method and differential constrains. Out solutions describe in particular the motion of the…

The classical problem of irrotational long waves on the surface of a shallow layer of an ideal fluid moving under the influence of gravity as well as surface tension is considered. A systematic procedure for deriving an equation for surface…

The paper's main goal is to compare the motion of solitary surface waves resulting from two similar but slightly different approaches. In the first approach, the numerical evolution of soliton surface waves moving over the uneven bottom is…

We consider a Boussinesq system describing one-dimensional internal waves which develop at the boundary between two immiscible fluids, and we restrict to its traveling waves. The method which yields explicitly all the elliptic or degenerate…

We investigate here the interactions of waves governed by a Boussinesq system with a partially immersed body allowed to move freely in the vertical direction. We show that the whole system of equations can be reduced to a transmission…

This work deals with the dynamics of higher-order rogue waves in a new integrable (2+1)-dimensional Boussinesq equation governing the evolution of high and steep gravity water waves. To achieve this objective, we construct rogue wave…

We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one dimensional waves, and consider the case of a flat bottom. Starting from the…

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume…

Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…

In this paper, we investigate the well-posedness of a nonlinear dispersive model with variable coefficients that describes the evolution of surface waves propagating through a one-dimensional shallow water channel of finite length with…

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…

We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…

The aim of this article is to derive surface wave models in the presence of surface tension and viscosity. Using the Navier-Stokes equations with a free surface, flat bottom and surface tension, we derive the viscous 2D Boussinesq system…

Boussinesq equation belongs to Korteweg-de Vries kind of equations (Han & Yarkony, 2011). Equation describes the motion of long waves in two dimensions under the gravitation (Han & Yarkony, 2011). Here, we differentiate u = u(x, t) to the…

We present the derivation of generic equations describing the long gravity waves in incompressible fluid with decaying effect. We show that in this theory the only restriction to the surface deviation is connected with the stability…

In this paper, we study the generalized Boussinesq equation as a model for the water wave problem with surface tension. Initially, we investigate the initial value problem within Sobolev spaces, deriving conditions under which solutions are…

Surface waves in a heated viscous fluid exhibit a long wave oscillatory instability. The nonlinear evolution of unidirectional waves is known to be described by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In the present work…

Three-dimensional geophysical fluids support both internal and boundary-trapped waves. To obtain the normal modes in such fluids we must solve a differential eigenvalue problem for the vertical structure (for simplicity, we only consider…