Computer Algebra Applied to a Solitary Waves Study

Abstract : We apply computer algebra techniques, such as algebraic computations of resultants and discriminants, certified drawing (with a guaranteed topology) of plane curves, to a problem in fluid dynamics: We investigate " capillary-gravity " solitary waves in shallow water, relying on the framework of the Serre-Green-Naghdi equations. So, we deal with two-dimensional surface waves, propagating in a shallow water of constant depth. By a differential elimination process, the study reduces to describing the solutions of an ordinary non linear first order differential equation, depending on two parameters. The paper is illustrated with examples and pictures computed with the computer algebra system Maple.
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ISSAC'2015, Jul 2015, Bath, United Kingdom. ACM, 2015, Proceedings ISSAC'2015. 〈10.1145/2755996.2756659〉
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Didier Clamond, Denys Dutykh, André Galligo. Computer Algebra Applied to a Solitary Waves Study. ISSAC'2015, Jul 2015, Bath, United Kingdom. ACM, 2015, Proceedings ISSAC'2015. 〈10.1145/2755996.2756659〉. 〈hal-01255412〉

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