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Zhang, Y. (2006) Solvability of a Class of Integro-Differential Equations and Connections to One Dimensional Inverse Problems. Journal of Mathematical Analysis and Applications, 321, 286-298.
https://doi.org/10.1016/j.jmaa.2005.08.016

has been cited by the following article:

• TITLE: A-Equation and Its Connections to Nonlinear Integrable System

  AUTHORS: Yilian Zhang

  KEYWORDS: Integrable System, A-Equation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.6, June 27, 2017

  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.