Connection Aspects of the Non-linear Schrödinger Equation

Abstract

Some geometrical features of the non-linear Schrödinger equation are studied and it is described how the Schrödinger equation can be obtained from the non-linear scattering equations. The SL(2, ℝ)-evalued elements of the matrix of the non-linear scattering problem are interpreted as matrix-valued forms. We calculate the curvature form with respect to a basis of the Lie algebra. If the curvature form equals zero then we obtain the non-linear Schrödinger equation.