A-Equation and Its Connections to Nonlinear Integrable System ()
ABSTRACT
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.
Share and Cite:
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.
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