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July  2020, 19(7): 3785-3785. doi: 10.3934/cpaa.2020167

Retraction: The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities

Editorial Office

Springfield, MO, United States

Published  June 2020

Communications on Pure and Applied Analysis, 19 (2020), 3785–3803

This article was accidentally posted online but only to be discovered that the same article had been published (see [1]) in the previous issue of the same journal. Thus this publication is retracted. The Editorial Office offers apologies for the confusion and inconvenience it might have caused.

Citation: Editorial Office. Retraction: The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3785-3785. doi: 10.3934/cpaa.2020167
References:
[1]

Shuai Zhang and Shaopeng Xu, The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities, Commun. Pur. Appl. Anal., 19 (2020), 3367-3385.  doi: 10.3934/cpaa.2020149.  Google Scholar

show all references

References:
[1]

Shuai Zhang and Shaopeng Xu, The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities, Commun. Pur. Appl. Anal., 19 (2020), 3367-3385.  doi: 10.3934/cpaa.2020149.  Google Scholar

[1]

Shuai Zhang, Shaopeng Xu. The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities. Communications on Pure & Applied Analysis, 2020, 19 (6) : 3367-3385. doi: 10.3934/cpaa.2020149
[2]

Yuanyuan Ren, Yongsheng Li, Wei Yan. Sharp well-posedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2018, 17 (2) : 487-504. doi: 10.3934/cpaa.2018027
[3]

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Carlos Banquet, Élder J. Villamizar-Roa. On the management fourth-order Schrödinger-Hartree equation. Evolution Equations & Control Theory, 2020, 9 (3) : 865-889. doi: 10.3934/eect.2020037
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Chuang Zheng. Inverse problems for the fourth order Schrödinger equation on a finite domain. Mathematical Control & Related Fields, 2015, 5 (1) : 177-189. doi: 10.3934/mcrf.2015.5.177
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Pavel I. Naumkin, Isahi Sánchez-Suárez. Asymptotics for the higher-order derivative nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (4) : 1447-1478. doi: 10.3934/cpaa.2021028
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Li Liang. Increasing stability for the inverse problem of the Schrödinger equation with the partial Cauchy data. Inverse Problems & Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469
[14]

Shouming Zhou. The Cauchy problem for a generalized $b$-equation with higher-order nonlinearities in critical Besov spaces and weighted $L^p$ spaces. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4967-4986. doi: 10.3934/dcds.2014.34.4967
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Paolo Antonelli, Daniel Marahrens, Christof Sparber. On the Cauchy problem for nonlinear Schrödinger equations with rotation. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 703-715. doi: 10.3934/dcds.2012.32.703
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Kihoon Seong. Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5437-5473. doi: 10.3934/cpaa.2020247
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Van Duong Dinh. Random data theory for the cubic fourth-order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (2) : 651-680. doi: 10.3934/cpaa.2020284
[18]

Benoît Pausader. The focusing energy-critical fourth-order Schrödinger equation with radial data. Discrete & Continuous Dynamical Systems, 2009, 24 (4) : 1275-1292. doi: 10.3934/dcds.2009.24.1275
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Zhong Wang. Stability of Hasimoto solitons in energy space for a fourth order nonlinear Schrödinger type equation. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 4091-4108. doi: 10.3934/dcds.2017174
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