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Long-Time Anderson Localization for the Nonlinear Schrödinger Equation Revisited

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Abstract

In this paper, we confirm the conjecture of Wang and Zhang (J Stat Phys 134 (5-6):953–968, 2009) in a long time scale, i.e., the displacement of the wavefront for 1D nonlinear random Schrödinger equation is of logarithmic order in time |t|.

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Notes

  1. [19] studied the NLSE with quasi-periodic potentials.

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Acknowledgements

H.C. was supported by NNSFC No. 11671066, No. 11401041 and NSFSP No. ZR2019MA062. Y.S. was supported by NNSFC No. 11901010 and Z.Z. was supported by NNSFC No. 11425103. The authors are very grateful to the anonymous referees for valuable suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Hongzi Cong

  2. College of Mathematics, Sichuan University, Chengdu, 610064, China

    Yunfeng Shi

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Zhifei Zhang

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  1. Hongzi Cong
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  2. Yunfeng Shi
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  3. Zhifei Zhang
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Correspondence to Yunfeng Shi.

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Communicated by Simone Warzel.

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Cong, H., Shi, Y. & Zhang, Z. Long-Time Anderson Localization for the Nonlinear Schrödinger Equation Revisited. J Stat Phys 182, 10 (2021). https://doi.org/10.1007/s10955-020-02677-y

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