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

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 and 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.

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.

[1]

Shuai Zhang, Shaopeng Xu. The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities. Communications on Pure and 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 and Applied Analysis, 2018, 17 (2) : 487-504. doi: 10.3934/cpaa.2018027

[3]

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Hongwei Wang, Amin Esfahani. On the Cauchy problem for a nonlocal nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022039

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Jun-ichi Segata. Initial value problem for the fourth order nonlinear Schrödinger type equation on torus and orbital stability of standing waves. Communications on Pure and Applied Analysis, 2015, 14 (3) : 843-859. doi: 10.3934/cpaa.2015.14.843

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Boling Guo, Jun Wu. Well-posedness of the initial-boundary value problem for the fourth-order nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3749-3778. doi: 10.3934/dcdsb.2021205

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Carlos Banquet, Élder J. Villamizar-Roa. On the management fourth-order Schrödinger-Hartree equation. Evolution Equations and 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 and 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 and 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 and Imaging, 2015, 9 (2) : 469-478. doi: 10.3934/ipi.2015.9.469

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Shouming Zhou. The Cauchy problem for a generalized $b$-equation with higher-order nonlinearities in critical Besov spaces and weighted $L^p$ spaces. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4967-4986. doi: 10.3934/dcds.2014.34.4967

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Kihoon Seong. Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation. Communications on Pure and 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 and 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 and 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 and Continuous Dynamical Systems, 2017, 37 (7) : 4091-4108. doi: 10.3934/dcds.2017174

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Jun-ichi Segata. Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1093-1105. doi: 10.3934/dcds.2010.27.1093

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