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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| Veröffentlicht in: | The European physical journal. D, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2009-06, Vol.53 (2), p.213-216 |
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| container_title | The European physical journal. D, Atomic, molecular, and optical physics |
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| creator | Zhao, D. He, X.-G. Luo, H.-G. |
| description | 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. |
| doi_str_mv | 10.1140/epjd/e2009-00051-7 |
| format | Article |
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| source | Springer Nature - Complete Springer Journals |
| 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 |
| title | Transformation from the nonautonomous to standard NLS equations |
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