Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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