The Finite Non-periodic Toda Lattice: a Geometric and Topological Viewpoint

In 1967, Japanese physicist Morikazu Toda published the seminal papers [78] and [79], exhibiting soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. In the decades that followed, Toda’s system of particles has been generalized in different directions, each with its own analytic, geometric, and topological characteristics that sets it apart from the others. These are known collectively as the Toda lattice. This survey describes and compares several versions of the finite non-periodic Toda lattice from the perspective of their geometry and topology.