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Dynamical behavior of analytical solutions and bifurcation analysis for a novel structured (2+1)-dimensional Kadomtsev-Petviashvili equation via analytic approach. [PDF]

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Ghayad MS, Hamada MY, Ahmed HM, Emadifar H, Ahmed KK.   +4 more
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On the Shallow Water Equations

Zeitschrift Fur Naturforschung - Section A Journal of Physical Sciences, 2017
AbstractWe studied the shallow water equations of nonlinear conservation laws. First we studied the parametrisation of nonlinear elementary waves and hence we present the solution to the Riemann problem. We also prove the uniqueness of the Riemann solution. The Riemann invariants are formulated.
Mahmoud Abdelrahman
exaly   +2 more sources

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.
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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
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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
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The Cauchy Problem of a Shallow Water Equation

Acta Mathematica Sinica, English Series, 2004
The authors consider the initial value problem for a fifth order shallow water equation in the nonperiodic case, as opposed to the previously considered periodic case. The equation studied has the same nonlinear terms as the well-known Fuchssteiner-Fokas-Camassa-Holm equation, and in this sense can be considered to be a higher order analogue of this ...
Liu, Xiaofeng, Jin, Yongyang
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On the weak solutions to a shallow water equation

Communications on Pure and Applied Mathematics, 2000
The authors obtain the existence of global-in-time weak solutions to the Cauchy problem for a one-dimensional formally integrable shallow-water equation of Camassa-Holm type. First, for an approximate viscous problem they establish uniform in viscosity energy estimates for the solution and its gradient.
Xin, Zhouping, Zhang, Ping
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Symmetric truncations of the shallow-water equations

Physical Review E, 1993
Conservation of potential vorticity in Eulerian fluids reflects [ital particle] [ital interchange] [ital symmetry] in the Lagrangian fluid version of the same theory. The algebra associated with this symmetry in the shallow-water equations is studied here, and we give a method for truncating the degrees of freedom of the theory which preserves a ...
, Rouhi, , Abarbanel
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Dispersive Nonlinear Shallow‐Water Equations

Studies in Applied Mathematics, 2009
A set of dispersive and hyperbolic depth‐averaged equations is obtained using a hyperbolic approximation of a chosen set of fully nonlinear and weakly dispersive Boussinesq‐type equations. These equations provide, at a reasonably reduced cost, both a physically sound description of the nearshore dynamics and a complete representation of dispersive and ...
Antuono, M., Liapidevskii, V., Brocchini, M.   +2 more
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An implicit wave equation model for the shallow water equations

Advances in Water Resources, 1984
In this paper an implicit numerical solution procedure for the shallow water equations is presented. It achieves efficiency through replacement of decompositions of a time-varying matrix by back substitutions for the solution of the equation system.
Ingemar P. E. Kinnmark, William G. Gray
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