Ulm 2004 – wissenschaftliches Programm
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MP: Theoretische und Mathematische Grundlagen der Physik
MP 2: Symmetrien,Integrabilit
ät und Quantisierung
MP 2.2: Fachvortrag
Montag, 15. März 2004, 14:25–14:50, SR 2203
Multiple Complexes and Integrable Models — •Folkert Müller-Hoissen1 and Aristophanes Dimakis2 — 1Max-Planck-Institut für Strömungsforschung, Bunsenstr. 10, D-37073 Göttingen — 2Dept. of Financial and Management Engineering, University of the Aegean, GR-82100 Chios, Greece
A parameter-dependent zero-curvature formulation of a completely
integrable (partial differential or difference) equation can be regarded as
a multiple complex given by linear maps Dk, k=1,2, … (acting on a
suitable linear space) which satisfy (∑k λk Dk)2 = 0 for all
λ ∈ R if and only if certain functions, on which the
Dk depend, solve the respective equation. In particular, this point of
view allows the construction of integrable models by starting with a
trivial complex and pursuing minimal ways of generating non-trivial
complexes. We show how previous work on bicomplexes [1,2] can be
generalized.
References:
1. A. Dimakis and F. Müller-Hoissen, J. Phys. A33 (2000) 6579-6591
[nlin.SI/0006029]
2. A. Dimakis and F. Müller-Hoissen, J. Phys. A34 (2001) 9163-9194
[nlin.SI/0104071]