Transformation from the nonautonomous to standard NLS equations

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 pre...

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Bibliographic Details
Published in:The European physical journal. D, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2009-06, Vol.53 (2), p.213-216
Main Authors: Zhao, D., He, X.-G., Luo, H.-G.
Format: Article
Language:English
Subjects:
Applications of Nonlinear Dynamics and Chaos Theory
Atomic
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Molecular
Nonlinear Dynamics
Nonlinear dynamics and nonlinear dynamical systems
Nonlinear optics
Optical and Plasma Physics
Optical solitons
nonlinear guided waves
Optics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Information Technology
Quantum Physics
Solitons
Spectroscopy/Spectrometry
Spintronics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary: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.
ISSN:1434-6060
1434-6079
DOI:10.1140/epjd/e2009-00051-7