JournalsprimsVol. 25 , No. 5DOI 10.2977/prims/1195172706

The Super-Toda Lattice Hierarchy

  • Kaoru Ikeda

    Tokyo Metropolitan University, Japan
The Super-Toda Lattice Hierarchy cover

Abstract

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.