Connection Aspects of the Non-linear Schrödinger Equation
Open Access
- 1 October 1981
- journal article
- Published by Walter de Gruyter GmbH in Zeitschrift für Naturforschung A
- Vol. 36 (10) , 1118-1119
- https://doi.org/10.1515/zna-1981-1018
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.Keywords
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