The super-Toda lattice (STL) hierarchy is introduced. The equivalence between the Lax representation and Zakharov-Shabat representation of the STL hierarchy is shown. Introducing the Lie superalgebra osp(∞ | ∞), the ortho-symplectic (OSp)-STL hierarchy is defined as well. These equations are solved through the Riemann-Hilbert decomposition of corresponding infinite dimensional Lie supergroups. An explicit representation of solutions is given by means of the super-τ field.
Cite this article
Kaoru Ikeda, The Super-Toda Lattice Hierarchy. Publ. Res. Inst. Math. Sci. 25 (1989), no. 5, pp. 829–845DOI 10.2977/PRIMS/1195172706