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- W3016959211 abstract "The Serre–Green–Naghdi (SGN) system is one of the most useful dispersive models for the description of long water waves having good mathematical and physical properties. First, the model is a mathematically justified approximation of the exact water-wave problem. Second, the SGN equations are the Euler–Lagrange equations derived from Hamilton’s principle of surface water waves with an approximate Lagrangian functional which appears naturally from the full Lagrangian. Finally, the equations are Galilean invariant which is necessary for physically relevant mathematical models. In this work, we derive the Whitham modulation equations for the SGN model and prove that these equations are strictly hyperbolic for any wave amplitude. This property can be interpreted by concluding that the periodic wave solutions of the SGN equations are modulationally stable. Numerical simulations of the full SGN equations are also shown, and these results confirm the theoretical stability results found using the Whitham modulation theory." @default.
- W3016959211 created "2020-04-24" @default.
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- W3016959211 date "2020-04-14" @default.
- W3016959211 modified "2023-09-25" @default.
- W3016959211 title "Hyperbolicity of the Modulation Equations for the Serre–Green–Naghdi Model" @default.
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- W3016959211 doi "https://doi.org/10.1007/s42286-020-00035-9" @default.
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