Results 231 to 240 of about 390,703 (296)

A shallow water equation on the circle

Communications on Pure and Applied Mathematics, 1999
The purpose of this paper is to study the spatially periodic case of the shallow water equation \[ \partial v/\partial t+ v\partial t/\partial x+\partial p/\partial x= 0\tag{1} \] in which the ``pressure'' \(p\) is \((1- d^2/dx^2)^{-1}(v^2+{1\over 2} v^{\prime 2})\). The equation has been much studied in recent years, starting with \textit{R.
A. Constantin, H. McKean
semanticscholar   +3 more sources

Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves

Applied Mathematics Letters, 2021
Yuan Shen
exaly   +2 more sources

Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation

Qualitative Theory of Dynamical Systems
Xin-Yi Gao, Gao Xin-Yi
exaly   +2 more sources

Orbital stability of solitary waves for a shallow water equation

Physica D: Nonlinear Phenomena, 2001
Adrian Constantin, Luc Molinet
exaly   +2 more sources

ON THE UNIQUENESS AND LARGE TIME BEHAVIOR OF THE WEAK SOLUTIONS TO A SHALLOW WATER EQUATION

Communications in Partial Differential Equations, 2002
Z. Xin, Ping Zhang
exaly   +2 more sources

A new highly nonlinear shallow water wave equation

Journal of Evolution Equations, 2016
Ronald Quirchmayr
exaly   +2 more sources

New periodic wave solutions of a time fractional integrable shallow water equation

Applied Ocean Research, 2019
In this paper, author employed Jacobi elliptic function expansion method to build the new wave solutions of time fractional modified Camassa–Holm equation which is completely integrable dispersive shallow-water equation.
A. Kurt
semanticscholar   +1 more source

The shallow water equations

Journal of Engineering Mathematics, 1970
In this paper a set of exact nonlinear equations is derived for gravity flows. By assuming the flow to be shallow and assuming the vertical acceleration to be small these equations reduce to the classical equations for long waves in shallow water.
openaire   +1 more source

On a numerical flux for the shallow water equations

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jirí Felcman, Oto Havle
openaire   +1 more source

Singular solutions for the shallow-water equations

IMA Journal of Applied Mathematics, 2012
We construct singular solutions for the shallow water system. The method of weak asymptotics is used to find singular solutions of the shallow-water system which can contain Dirac-δ distributions (Espinosa & Omel'yanov, 2005). Complex-valued approximations which become real-valued in the distributional limit are shown to extend the range of possible ...
Kalisch, Henrik, Mitrović, Darko
openaire   +2 more sources