Computer algebra applied to a solitary waves study

Didier Clamond; Denys Dutykh; André Galligo

doi:10.1145/2755996.2756659

Computer algebra applied to a solitary waves study

Didier Clamond, Denys Dutykh, André Galligo

Mathematics

Université de Nice - Sophia Antipolis

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

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.

Original language	British English
Title of host publication	ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation
Pages	125-132
Number of pages	8
ISBN (Electronic)	9781450334358
DOIs	https://doi.org/10.1145/2755996.2756659
State	Published - 24 Jun 2015
Event	40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015 - Bath, United Kingdom Duration: 6 Jul 2015 → 9 Jul 2015

Publication series

Name	Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
Volume	2015-June

Conference

Conference	40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015
Country/Territory	United Kingdom
City	Bath
Period	6/07/15 → 9/07/15

Keywords

Certified drawing
Classification
Differential elimination
Discriminants
Non linear differential equation
Peakon
Plane curves
Plane phase analysis
Resultants
Solitary waves

Access to Document

10.1145/2755996.2756659

Cite this

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title = "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.",

keywords = "Certified drawing, Classification, Differential elimination, Discriminants, Non linear differential equation, Peakon, Plane curves, Plane phase analysis, Resultants, Solitary waves",

author = "Didier Clamond and Denys Dutykh and Andr{\'e} Galligo",

year = "2015",

month = jun,

day = "24",

doi = "10.1145/2755996.2756659",

language = "British English",

series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",

pages = "125--132",

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Clamond, D, Dutykh, D & Galligo, A 2015, Computer algebra applied to a solitary waves study. in ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, vol. 2015-June, pp. 125-132, 40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015, Bath, United Kingdom, 6/07/15. https://doi.org/10.1145/2755996.2756659

Computer algebra applied to a solitary waves study. / Clamond, Didier; Dutykh, Denys; Galligo, André.
ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation. 2015. p. 125-132 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; Vol. 2015-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Dutykh, Denys

AU - Galligo, André

PY - 2015/6/24

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N2 - 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.

AB - 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.

KW - Certified drawing

KW - Classification

KW - Differential elimination

KW - Discriminants

KW - Non linear differential equation

KW - Peakon

KW - Plane curves

KW - Plane phase analysis

KW - Resultants

KW - Solitary waves

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M3 - Conference contribution

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T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

SP - 125

EP - 132

BT - ISSAC 2015 - Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation

T2 - 40th ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2015

Y2 - 6 July 2015 through 9 July 2015

ER -

Computer algebra applied to a solitary waves study

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Keywords

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