Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 4, September 2020, Pages 529 - 549

Minimal surfaces associated with orthogonal polynomials

Authors
Vincent Chalifour
Departement of mathematics and statistics, Université de Montréal, C. P. 6128, Succ. Centre-ville, Montréal, Québec, H3C 3J7, Canada,chalifour@dms.umontreal.ca
Alfred Michel Grundland*
1Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128, Succ. Centre-ville, Montréal, Québec, H3C 3J7, Canada
2Departement of Mathematics and Computer Science, Université du Québec, CP500, Trois-Rivières, Québec, G9A 5H7, Canada,grundlan@crm.umontreal.ca
*Corresponding author.
Corresponding Author
Alfred Michel Grundland
Received 17 January 2019, Accepted 3 December 2019, Available Online 4 September 2020.
DOI
10.1080/14029251.2020.1819599How to use a DOI?
Keywords
Integrable system; soliton surface; minimal surface; orthogonal polynomial; Weierstrass immersion formula; Sym-Tafel immersion formula; CMC surface
Abstract

This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces approach defined by the Enneper-Weierstrass formula for immersion and the solutions of the Gauss-Weingarten equations for moving frames, we derive the three-dimensional numerical representation for these polynomials. We illustrate the theoretical results for several examples, including the Bessel, Legendre, Laguerre, Chebyshev and Jacobi functions. In each case, we generate a numerical representation of the surface using the Mathematica symbolic software.

Copyright
© 2020 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 4
Pages
529 - 549
Publication Date
2020/09/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1819599How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Vincent Chalifour
AU  - Alfred Michel Grundland
PY  - 2020
DA  - 2020/09/04
TI  - Minimal surfaces associated with orthogonal polynomials
JO  - Journal of Nonlinear Mathematical Physics
SP  - 529
EP  - 549
VL  - 27
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1819599
DO  - 10.1080/14029251.2020.1819599
ID  - Chalifour2020
ER  -