Eur. Phys. J. D 53, 213-216 (2009)
https://doi.org/10.1140/epjd/e2009-00051-7

Transformation from the nonautonomous to standard NLS equations

¹ School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P.R. China
² Center for Interdisciplinary Studies, Lanzhou University, Lanzhou, 730000, P.R. China
³ Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou, 730000, P.R. China
⁴ Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100080, P.R. China

Corresponding author: ^a luohg@itp.ac.cn

Received: 30 September 2008
Revised: 11 December 2008
Published online: 18 February 2009

Abstract

In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schrödinger (NLS) equation. An integrable condition is first obtained by the Painlevé analysis, which is shown to be consistent with that obtained by the Lax pair method. Under this condition, we present a general transformation, which can directly convert all allowed exact solutions of the standard NLS equation into the corresponding exact solutions of the nonautonomous NLS equation. The method is quite powerful since the standard NLS equation has been well studied in the past decades and its exact solutions are vast in the literature. The result provides an effective way to control the soliton dynamics. Finally, the fundamental bright and dark solitons are taken as examples to demonstrate its explicit applications.