Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame-Reference-Cited by-同舟云学术

Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame

Published:2020-01-22 Issue:14 Volume:2021 Page:11050-11092
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Wang Bao¹²³,Chang Xiang-Ke¹²,Hu Xing-Biao¹²,Li Shi-Hao¹²⁴

Affiliation:

1. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, PR China

2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China

3. Department of Mathematics and Statistics, Brock University, St. Catharines, ON Canada L2S 3A1

4. School of Mathematics and Statistics, the University of Melbourne, Victoria 3010, Australia

Abstract

Abstract In this paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference invariants, and this approach enables one to obtain the corresponding discrete invariant curve flows simultaneously. Several examples in the cases of centro-affine plane, pseudo-Euclidean plane, and high-dimensional centro-affine space are presented.

Funder

National Natural Science Foundation of China

Youth Innovation Promotion Association CAS

ARC Centre of Excellence for Mathematical and Statistical frontiers

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/14/11050/38934046/rnz379.pdf

Reference51 articles.

1. Solitons, Nonlinear Evolution Equations and Inverse Scattering

2. New integrable nonlinearities from affine geometry;Antonowicz;Phys. Lett. A,1985

3. The theory of differential invariants and KdV Hamiltonian evolutions;Beffa;Bull. Soc. Math. France,1999

4. Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces;Beffa;Proc. Amer. Math. Soc.,2006

5. Discrete moving frames on lattice varieties and lattice-based multispaces;Beffa;Found. Comput. Math.,2018

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Hungry Lotka–Volterra lattice under nonzero boundaries, block‐Hankel determinant solution, and biorthogonal polynomials;Studies in Applied Mathematics;2023-07-19