Results 251 to 260 of about 390,703 (296)

The shallow-water equations

2009
We now enter the realm of hyperbolic equations. Instead of starting with an introduction to numerical methods for hyperbolic equations in general, we prefer to begin by plunging into the particular case of the shallow-water equations. Other hyperbolic equations will be considered in Chapters 9 and 10.
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SLOW EIGENMODES OF THE SHALLOW-WATER EQUATIONS

Waves and Stability in Continuous Media, 2002
We present a survey of recent work on the lowest end of the eigenmode spectrum of the shallow water equations in a rotating reference frame. The results are complemented with numerical simulations of the fully nonlinear equations. Having care of using physically correct, mass-conserving boundary conditions, a description in terms of slow eigenmodes ...
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Studies on certain bilinear form, N-soliton, higher-order breather, periodic-wave and hybrid solutions to a (3+1)-dimensional shallow water wave equation with time-dependent coefficients

Nonlinear dynamics, 2022
Yuan Shen, B. Tian, Shao-Hua Liu, Tian-Yu Zhou   +3 more
semanticscholar   +1 more source

Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves

Nonlinear dynamics, 2022
Fei-Yan Liu, Yi Gao, Xin Yu, Cui-Cui Ding   +3 more
semanticscholar   +1 more source

A shock solution for the nonlinear shallow water equations

Journal of Fluid Mechanics, 2010
A global shock solution for the nonlinear shallow water equations (NSWEs) is found by assigning proper seaward boundary data that preserve a constant incoming Riemann invariant during the shock wave evolution. The correct shock relations, entropy conditions and asymptotic behaviour near the shoreline are provided along with an in-depth analysis of the ...
Antuono, Matteo
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Derivation of the Shallow Water Equations

2020
This chapter presents a derivation of the shallow water equations, which describe flows where horizontal length-scales are much larger than the vertical. This occurs when hydrodynamic processes are small in comparison to gravity effects, and is therefore appropriate for tidal flows in channels where the tidal wavelength \(\lambda _w\) is greater than ...
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The shallow water equation

Abstract This chapter first presents a simple derivation of the shallow water equation. It then proposes an implicit (time) and centered (space) discretization and tests it in one dimension. The chapter then examines solutions to look at front steepening and testing the dependence of the wave velocity on the water column depth expected ...
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On a Shallow Water Equation Perturbed in Schwartz Class

Mathematical Physics, Analysis and Geometry, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

, 2020
Ji-Huan He
semanticscholar   +1 more source

The Cauchy problem of a weakly dissipative shallow water equation

, 2019
Sen Ming, S. Lai, Yeqin Su
semanticscholar   +1 more source