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Painlevé analysis of the damped, driven nonlinear Schrödinger equation

Published online by Cambridge University Press:  14 November 2011

Peter A. Clarkson
Peter A. Clarkson
Affiliation:
Mathematics Department, Birmingham University, Birmingham B15 2TT, U.K.
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Synopsis

In this paper we apply the Painlevé tests to the damped, driven nonlinear Schrödinger equation

where a(x, t) and b(x, t) are analytic functions of x and t, todetermine under what conditions the equation might be completely integrable. It is shown that (0.1) can pass the Painlevé tests only if

where α0(t),α1(t) and β(t) are arbitrary, real analytic functions of time. Furthermore, it is shown that in this special case, (0.1) may be transformed into the original nonlinear Schrödinger equation, which is known to be completely integrable.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 1-2 , 1988 , pp. 109 - 126
Copyright
Copyright © Royal Society of Edinburgh 1988

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