Author(s)

Yilian Zhang

Department of Mathematical Science, University of South Carolina, Aiken, SC, USA.

A novel approach to inverse spectral theory for Schrödinger Equation operators on a half-line was first introduced by Barry Simon and actively studied in recent literatures. The remarkable discovery is a new object A-function and intergo-differential Equation (called A-Equation) it satisfies. Inverse problem of reconstructing potential is then directly connected to finding solutions of A-Equation. In this work, we present a large class of exact solutions to A-Equation and reveal the connection to a class of arbitrarily large systems of nonlinear ordinary differential Equations. This non-linear system turns out to be C-integrable in the sense of F. Calogero. Integration scheme is proposed and the approach is illustrated in several examples.

Integrable System, A-Equation

Zhang, Y. (2017) A-Equation and Its Connections to Nonlinear Integrable System. Journal of Applied Mathematics and Physics, 5, 1320-1334. doi: 10.4236/jamp.2017.56110.