Abstract
We apply computer algebra techniques and drawing with a guaranteed topology of plane curves, to the study of internal gravity solitary waves in shallow water, relying on an improved framework of the Serre-Green-Naghdi equations. By a differential elimination process, the study reduces to describing the solutions of a special type of ordinary non linear first order differential equation, depending on parameters. The analysed constraints imply a reduction of the allowed configurations, and we can provide a topological classification of the phase plane curves. So, special behaviors are detected even if they appear in tiny domain of the parameter space. The paper is illustrated with examples and pictures.
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Acknowledgements
We thank our colleague Denys Dutykh for useful discussions and his important involvement in a preliminary version of this work four years ago.
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Galligo, A., Clamond, D. (2023). Certified Study of Internal Solitary Waves. In: Boulier, F., England, M., Kotsireas, I., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2023. Lecture Notes in Computer Science, vol 14139. Springer, Cham. https://doi.org/10.1007/978-3-031-41724-5_5
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DOI: https://doi.org/10.1007/978-3-031-41724-5_5
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