Farwell, Ruth; Minami, Masatsugu One-dimensional Toda molecule. I: General solution. (English) Zbl 1171.53341 Prog. Theor. Phys. 69, No. 4, 1091-1115 (1983). Summary: A mechanism is presented for producing explicitly the general solutions to the one-dimensional Toda molecule equations associated with the classical complex Lie algebras of rank \(N\): \(sl (N+1,\mathbb{C})\), \(so(2N+1,\mathbb{C})\), \(sp(N,\mathbb{C})\) and \(so (2N,\mathbb{C})\). The method itself is applicable, however, to any semi-simple Lie algebra. A particular feature of our solutions is their description in terms of the “initial data”, which is consistent with the fact that the one-dimensional Toda molecule equation is a Newtonian equation of motion. The solutions for the algebras associated with \(SU(2)\), \(SU(3)\) and \(Sp(2)\) are given explicitly. Cited in 1 ReviewCited in 7 Documents MSC: 53C80 Applications of global differential geometry to the sciences 17B20 Simple, semisimple, reductive (super)algebras × Cite Format Result Cite Review PDF Full Text: DOI