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SIGMA 2 (2006), 022, 11 pages nlin.SI/0602038
https://doi.org/10.3842/SIGMA.2006.022
Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras
Vladimir S. Gerdjikov a and Georgi G. Grahovski a, b
a) Institute for Nuclear Research and Nuclear
Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria
b) Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise,
2 Avenue Adolphe Chauvin, F-95302 Cergy-Pontoise Cedex, France
Received December 19, 2005, in final form February 05, 2006; Published online February 17, 2006
Abstract
The construction of a family of real Hamiltonian forms
(RHF) for the special class of affine 1+1-dimensional Toda
field theories (ATFT) is reported. Thus the method, proposed in
[1] for systems with finite number of degrees of freedom is
generalized to infinite-dimensional Hamiltonian systems. The
construction method is illustrated on the explicit nontrivial
example of RHF of ATFT related to the exceptional algebras E6 and E7.
The involutions of the local integrals of
motion are proved by means of the classical R-matrix approach.
Key words:
solitons; affine Toda field theories; Hamiltonian systems.
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