Journal of Nonlinear Mathematical Physics

Volume 10, Issue Supplement 2, December 2003, Pages 194 - 208

Lattice Geometry of the Discrete Darboux, KP, BKP and CKP Equations. Menelaus' and Carnot's Theorems

Authors
Wolfgang Karl Schief
Corresponding Author
Wolfgang Karl Schief
Available Online 1 December 2003.
DOI
10.2991/jnmp.2003.10.s2.17How to use a DOI?
Abstract

Möbius invariant versions of the discrete Darboux, KP, BKP and CKP equations are derived by imposing elementary geometric constraints on an (irregular) lattice in a three-dimensional Euclidean space. Each case is represented by a fundamental theorem of plane geometry. In particular, classical theorems due to Menelaus and Carnot are employed. An interpretation of the discrete CKP equation as a permutability theorem is also provided.

Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
10 - Supplement 2
Pages
194 - 208
Publication Date
2003/12/01
ISBN
91-974824-0-4
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2003.10.s2.17How to use a DOI?
Copyright
© 2006, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Wolfgang Karl Schief
PY  - 2003
DA  - 2003/12/01
TI  - Lattice Geometry of the Discrete Darboux, KP, BKP and CKP Equations. Menelaus' and Carnot's Theorems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 194
EP  - 208
VL  - 10
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.s2.17
DO  - 10.2991/jnmp.2003.10.s2.17
ID  - Schief2003
ER  -