Geodesic
Real Hamiltonian forms of affine Toda field theories: Spectral aspects
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 190-212

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The paper is devoted to real Hamiltonian forms of $2$-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of “reductions” of Hamiltonian systems, similar to real forms of semisimple Lie algebras. Examples of real Hamiltonian forms of affine Toda field theories related to exceptional complex untwisted affine Kac–Moody algebras are studied. Along with the associated Lax representations, we also formulate the relevant Riemann–Hilbert problems and derive the minimal sets of scattering data that uniquely determine the scattering matrices and the potentials of the Lax operators.
Keywords: real Hamiltonian form, 2-dimensional Toda field theory, spectral properties of Lax operators.
Mots-clés : exceptional Lie algebras 
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     author = {V. S. Gerdjikov and G. G. Grahovski and A. A. Stefanov},
     title = {Real {Hamiltonian} forms of affine {Toda} field theories: {Spectral} aspects},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {2},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a2/}
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V. S. Gerdjikov; G. G. Grahovski; A. A. Stefanov. Real Hamiltonian forms of affine Toda field theories: Spectral aspects. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 190-212. http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a2/