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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 A E Abdelrahman
exaly   +2 more sources

Global Weak Solutions for a Shallow Water Equation

Communications in Mathematical Physics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Adrian Constantin, Luc Molinet
exaly   +2 more sources

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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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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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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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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