The quantum Gelfand-Levitan equation and nonlinear Schrodinger equation

Abstract

The author investigates the analysis on which the quantum Gelfand-Levitan equation depends. He derives two different forms of the quantum Gelfand-Levitan equation using different Bethe ansatz creation-annihilation operators, but shows that they lead to equivalent results. He also derives inversion relations for solutions of the Zakharov-Shabat equations and relates them to Wronskians. This paper continues an investigation of the quantum inverse method and the nonlinear Schrodinger equation begun previously by Davies and Kieu (1986).