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An integrable time-dependent non-linear Schrödinger equation

P. A. Horváthy·J. -C. Yéra
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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 $F=\const$.) by means of a time-dependent on-linear transformation, related to the conformal properties of non-relativistic space-time.

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P. A. Horváthy, J. -C. Yéra. 1998-06-30. An integrable time-dependent non-linear Schrödinger equation. https://arxiv.org/abs/math-ph/9806017

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