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Geometric analysis and onset of chaos for the resonant nonlinear Schrödinger system

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Abstract

In this paper, Jacobi stability of a resonant nonlinear Schrödinger (RNS) system is studied by the KCC theory, which is also called differential geometric method. The RNS system is transformed into an equivalent planar differential system by traveling wave transformation, then the Lyapunov stability of equilibrium points of the planar system is analyzed. By constructing geometric invariants, we analyze and discuss the Jacobi stability of three equilibrium points. The results show that the zero point is always Jacobi stable, while the Jacobi stability of the other nonzero equilibrium points are determined by the values of the parameters. In addition, the focusing tendency towards trajectories around the equilibrium points are studied by the dynamical behavior of deviation vector. Finally, numerical results show that the system presents quasi-periodic and chaotic phenomena under periodic disturbances.

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  • 13 January 2022

    This article was revised due to wrong given names for two of the authors of reference 19 in the reference list.

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Acknowledgements

The authors thank the reviewers for their constructive and pertinent suggestions for improving the manuscript. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11961074, 11971414), Natural Science Foundation of Guangxi Province (Grant No. 2018GXNSFDA281028), the Excellent Youth Foundation of SINOPEC (P20009), the High Level Innovation Team Program from Guangxi Higher Education Institutions of China (Document No. [2018] 35) and the research ability enhancement project of young and middle-aged teachers in Guangxi colleges and universities (Grant No. 2020KY14008).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Ting Lai & Chunsheng Feng

  2. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, People’s Republic of China

    Yongjian Liu & Aimin Liu

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  1. Ting Lai
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  2. Chunsheng Feng
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  3. Yongjian Liu
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  4. Aimin Liu
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Correspondence to Yongjian Liu.

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Lai, T., Feng, C., Liu, Y. et al. Geometric analysis and onset of chaos for the resonant nonlinear Schrödinger system. Eur. Phys. J. Spec. Top. 231, 2133–2142 (2022). https://doi.org/10.1140/epjs/s11734-021-00398-1

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