On the nonlinear dynamics of the traveling-wave solutions of the Serre system
Abstract
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes a high-order finite-element method with smooth, periodic splines in space and explicit Runge-Kutta methods in time. Other forms of solutions such as cnoidal waves and dispersive shock waves are also considered. The differences between solutions of the Serre equations and the Euler equations are also studied.
Domains
Fluid mechanics [physics.class-ph] Fluids mechanics [physics.class-ph] Global Changes Exactly Solvable and Integrable Systems [nlin.SI] Pattern Formation and Solitons [nlin.PS] Hydrology Fluid Dynamics [physics.flu-dyn] Atmospheric and Oceanic Physics [physics.ao-ph] Numerical Analysis [math.NA] Analysis of PDEs [math.AP] Computational Physics [physics.comp-ph] Ocean, Atmosphere Geophysics [physics.geo-ph] Geophysics [physics.geo-ph]
Origin : Files produced by the author(s)
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