An integrable time-dependent non-linear Schrödinger equation
P. A. Horváthy, J. -C. Yéra
Abstract
The cubic non-linear Schrödinger equation (NLS), where the coefficient of the non-linear term can be a function F(t,x), is shown to pass the Painlevé test of Weiss, Tabor, and Carnevale only for F=(a+bt)-1, where a and b constants. This is explained by transforming the time-dependent system into the ordinary NLS (with F=.) by means of a time-dependent on-linear transformation, related to the conformal properties of non-relativistic space-time.
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