The Super-Toda Lattice Hierarchy

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 $\mathrm{osp}(\infty |\infty )$, 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-$\tau$ field.