Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-07-02
Nonlinear Sciences
Exactly Solvable and Integrable Systems
36 pages, 15 figures
Scientific paper
A remarkable connection between soliton theory and an important and beautiful branch of the theory of graphical statics developed by Maxwell and his contemporaries is revealed. Thus, it is demonstrated that reciprocal triangles which constitute the simplest pair of reciprocal figures representing both a framework and a self-stress encapsulate the integrable discrete BKP equation and its Schwarzian version. The inherent Moebius invariant nature of the Schwarzian BKP equation is then exploited to define reciprocity in an inversive geometric setting. Integrable pairs of lattices of non-trivial combinatorics consisting of reciprocal triangles and their natural generalizations are discussed. Particular reductions of these BKP lattices are related to the integrable discrete versions of Darboux's 2+1-dimensional sine-Gordon equation and the classical Tzitzeica equation of affine geometry. Furthermore, it is shown that octahedral figures and their hexahedral reciprocals as considered by Maxwell likewise give rise to discrete integrable systems and associated integrable lattices.
Konopelchenko Boris. G.
Schief W. K.
No associations
LandOfFree
Reciprocal figures, graphical statics and inversive geometry of the Schwarzian BKP hierarchy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Reciprocal figures, graphical statics and inversive geometry of the Schwarzian BKP hierarchy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reciprocal figures, graphical statics and inversive geometry of the Schwarzian BKP hierarchy will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-286677