Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics

Kay Kirkpatrick;  Benjamin Schlein;  Gigliola Staffilani

doi:10.1353/ajm.2011.0004

Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics

American Journal of Mathematics ◽

10.1353/ajm.2011.0004 ◽

2011 ◽

Vol 133 (1) ◽

pp. 91-130 ◽

Cited By ~ 50

Author(s):

Kay Kirkpatrick ◽

Benjamin Schlein ◽

Gigliola Staffilani

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Quantum Dynamics ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Many Body ◽

Nonlinear Schrödinger ◽

Many Body Quantum Dynamics

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Stability of one and two-dimensional spatial solitons in a cubic-quintic-septimal nonlinear Schrödinger equation with fourth-order diffraction and PT-symmetric potentials

Wave Motion ◽

10.1016/j.wavemoti.2021.102810 ◽

2021 ◽

pp. 102810

Author(s):

Boubakary Abdou ◽

Fabien II Ndzana ◽

Latchio Tiofack Gaston ◽

Alidou Mohamadou

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Spatial Solitons ◽

Nonlinear Schrödinger ◽

Order Diffraction

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Simple multiple explode–decay mode solutions of a two‐dimensional nonlinear Schrödinger equation

Journal of Mathematical Physics ◽

10.1063/1.525361 ◽

1982 ◽

Vol 23 (3) ◽

pp. 417-420 ◽

Cited By ~ 9

Author(s):

Akira Nakamura

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Decay Mode ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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Exact solutions of a two-dimensional nonlinear Schrödinger equation

Applied Mathematics Letters ◽

10.1016/j.aml.2011.09.030 ◽

2012 ◽

Vol 25 (4) ◽

pp. 687-691 ◽

Cited By ~ 96

Author(s):

Aly R. Seadawy

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation

Theoretical and Mathematical Physics ◽

10.1007/s11232-014-0154-1 ◽

2014 ◽

Vol 179 (1) ◽

pp. 452-461 ◽

Cited By ~ 9

Author(s):

D. E. Pelinovsky ◽

E. A. Rouvinskaya ◽

O. E. Kurkina ◽

B. Deconinck

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Short Wave ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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One Dimensionally Alligned Decay Mode Solutions of the Two Dimensional Nonlinear Schrödinger Equation

Journal of the Physical Society of Japan ◽

10.1143/jpsj.50.2469 ◽

1981 ◽

Vol 50 (8) ◽

pp. 2469-2470 ◽

Cited By ~ 9

Author(s):

Akira Nakamura

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Decay Mode ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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An energy-preserving Crank–Nicolson Galerkin spectral element method for the two dimensional nonlinear Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.05.025 ◽

2018 ◽

Vol 344 ◽

pp. 245-258 ◽

Cited By ~ 4

Author(s):

Haochen Li ◽

Zhenguo Mu ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Spectral Element Method ◽

Spectral Element ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Element Method ◽

Crank Nicolson

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Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation

Annales de l Institut Henri Poincaré C Analyse non linéaire ◽

10.1016/j.anihpc.2018.10.007 ◽

2019 ◽

Vol 36 (5) ◽

pp. 1201-1235 ◽

Cited By ~ 5

Author(s):

Christian Brennecke ◽

Phan Thành Nam ◽

Marcin Napiórkowski ◽

Benjamin Schlein

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Quantum Dynamics ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Exact Solutions of the Two-Dimensional Cubic-Quintic Nonlinear Schrödinger Equation with Spatially Modulated Nonlinearities

Communications in Theoretical Physics ◽

10.1088/0253-6102/59/3/08 ◽

2013 ◽

Vol 59 (3) ◽

pp. 290-294 ◽

Cited By ~ 6

Author(s):

Xiang Song ◽

Hua-Mei Li

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Quintic Nonlinear Schrödinger Equation

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A Galerkin energy-preserving method for two dimensional nonlinear Schrödinger equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2017.11.056 ◽

2018 ◽

Vol 324 ◽

pp. 16-27

Author(s):

Haochen Li ◽

Chaolong Jiang ◽

Zhongquan Lv

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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Publisher's Note: Exact spatial soliton solutions of the two-dimensional generalized nonlinear Schrödinger equation with distributed coefficients [Phys. Rev. A78, 023821 (2008)]

Physical Review A ◽

10.1103/physreva.78.039906 ◽

2008 ◽

Vol 78 (3) ◽

Cited By ~ 10

Author(s):

Wei-Ping Zhong ◽

Rui-Hua Xie ◽

Milivoj Belić ◽

Nikola Petrović ◽

Goong Chen

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Spatial Soliton ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Generalized Nonlinear Schrödinger Equation

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