Results 31 to 40 of about 88 (42)

On the origin of the Korteweg-de Vries equation [PDF]

Forum der Berliner Mathematischen Gesellschaft, Band 19, Dezember 2011, pp. 171-195, 2006
The Korteweg-de Vries equation has a central place in a model for waves on shallow water and it is an example of the propagation of weakly dispersive and weakly nonlinear waves. Its history spans a period of about sixty years, starting with experiments of Scott Russell in 1834, followed by theoretical investigations of, among others, Lord Rayleigh and ...
arxiv  

Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise [PDF]

arXiv, 2009
We consider a randomly perturbed Korteweg-de Vries equation. The perturbation is a random potential depending both on space and time, with a white noise behavior in time, and a regular, but stationary behavior in space. We investigate the dynamics of the soliton of the KdV equation in the presence of this random perturbation, assuming that the ...
arxiv  

Asymptotic linear stability of solitary water waves [PDF]

arXiv, 2010
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 above by a free surface under the influence of gravity neglecting surface tension.
arxiv  

On the onset of filamentation on two-dimensional vorticity interfaces [PDF]

arXiv
We study an asymptotic nonlinear model for filamention on two-dimensional vorticity interfaces. Different re-formulations of the model equation reveal its underlying structural properties. They enable us to construct global weak solutions and to prove the existence of traveling waves.
arxiv  

Notes on solitary-wave solutions of Rosenau-type equations [PDF]

arXiv
The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of three different forms are derived. The results depend on some conditions on the speed of the waves with respect to
arxiv  

Main topics of the NumHyp-2015' discussion session [PDF]

arXiv
Three main topics were raised in this discussion session, which took place on the 19th of June at the NumHyp-2015 meeting: nonlinear resonance for 1D systems of balance laws, dispersive extensions of standard hyperbolic conservation laws, and the validation of weakly dispersive shallow water wave models. An introductory overview with many bibliographic
arxiv  

Remarks on solitary waves in equations with nonlocal cubic terms [PDF]

arXiv
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where $\Lambda^s, \Lambda^r$ are Bessel-type Fourier multipliers. The linear operator may be of low fractional order, $s>
arxiv  

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A Coupled Model for Wave Run-up Simulation

, 2017
Simplified models like the shallow water equations (SWE) are commonly adopted for describing a wide range of free surface flow problems, like flows in rivers, lakes, estuaries, or coastal areas. In the literature, numerical methods for the SWE are mostly
Iryanto, S. R. Pudjaprasetya
semanticscholar   +1 more source

Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking

, 2016
In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary ...
Magnar Bjørkavûag, H. Kalisch, Zahra Khorsand, D. Mitsotakis   +3 more
semanticscholar   +1 more source

Numerical study of staggered scheme for viscous Saint-Venant equations

, 2014
This paper describes a numerical scheme for approximate the viscous Saint-Venant equations. This scheme is called staggered grid scheme which is a robust, simple and strightforward scheme for viscous SaintVenant equations. Some numerical simulations have
P. H. Gunawan
semanticscholar   +1 more source