The nonlinear Schrödinger equation as a resonant normal form

Dario Bambusi;  ; A. Carati; A. Ponno;  ;

doi:10.3934/dcdsb.2002.2.109

The nonlinear Schrödinger equation as a resonant normal form

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2002.2.109 ◽

2002 ◽

Vol 2 (1) ◽

pp. 109-128

Author(s):

Dario Bambusi ◽

◽

A. Carati ◽

A. Ponno ◽

◽

...

Keyword(s):

Normal Form ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Resonant Normal Form

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Normal form for the symmetry-breaking bifurcation in the nonlinear Schrödinger equation

Journal of Differential Equations ◽

10.1016/j.jde.2012.07.007 ◽

2012 ◽

Vol 253 (10) ◽

pp. 2796-2824 ◽

Cited By ~ 15

Author(s):

D.E. Pelinovsky ◽

T.V. Phan

Keyword(s):

Normal Form ◽

Schrödinger Equation ◽

Symmetry Breaking ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Symmetry Breaking Bifurcation

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Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrödinger equation on the circle

Annales de l Institut Henri Poincaré C Analyse non linéaire ◽

10.1016/j.anihpc.2016.10.003 ◽

2017 ◽

Vol 34 (5) ◽

pp. 1273-1297 ◽

Cited By ~ 4

Author(s):

Jaywan Chung ◽

Zihua Guo ◽

Soonsik Kwon ◽

Tadahiro Oh

Keyword(s):

Normal Form ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation ◽

Form Approach

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Normal Form of Nonlinear Schrödinger Equation

Journal of the Physical Society of Japan ◽

10.1143/jpsj.58.4322 ◽

1989 ◽

Vol 58 (12) ◽

pp. 4322-4328 ◽

Cited By ~ 27

Author(s):

Toshiyuki Kano

Keyword(s):

Normal Form ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Birkhoff normal form for the nonlinear Schrödinger equation

Rendiconti Lincei - Matematica e Applicazioni ◽

10.4171/rlm/653 ◽

2013 ◽

Vol 24 (2) ◽

pp. 215-228

Author(s):

Walter Craig ◽

Alessandro Selvitella ◽

Yun Wang

Keyword(s):

Normal Form ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Birkhoff Normal Form ◽

Nonlinear Schrödinger

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Normal form for the onset of collapse: The prototypical example of the nonlinear Schrödinger equation

Physical Review E ◽

10.1103/physreve.104.044202 ◽

2021 ◽

Vol 104 (4) ◽

Author(s):

S. J. Chapman ◽

M. Kavousanakis ◽

I. G. Kevrekidis ◽

P. G. Kevrekidis

Keyword(s):

Normal Form ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Nonlinear Schrödinger Equation-Based Adjoint Sensitivity Analysis

2020 International Applied Computational Electromagnetics Society Symposium (ACES) ◽

10.23919/aces49320.2020.9196096 ◽

2020 ◽

Author(s):

Mahmoud M. T. Maghrabi ◽

Mohamed H. Bakr ◽

Shiva Kumar

Keyword(s):

Sensitivity Analysis ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Adjoint Sensitivity Analysis ◽

Adjoint Sensitivity ◽

Nonlinear Schrödinger

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Higher-order nonlinear Schrödinger equation in 2D case

Tohoku Mathematical Journal ◽

10.2748/tmj/1585101619 ◽

2020 ◽

Vol 72 (1) ◽

pp. 15-37

Author(s):

Nakao Hayashi ◽

Pavel I. Naumkin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Some properties of small perturbations against a stationary solution of the nonlinear Schrödinger equation

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2019.109570 ◽

2020 ◽

Vol 132 ◽

pp. 109570

Author(s):

Mikhail N. Smolyakov

Keyword(s):

Schrödinger Equation ◽

Stationary Solution ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Small Perturbations ◽

Nonlinear Schrödinger

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Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.4931710 ◽

2015 ◽

Vol 25 (10) ◽

pp. 103114 ◽

Cited By ~ 26

Author(s):

D. J. Kedziora ◽

A. Ankiewicz ◽

A. Chowdury ◽

N. Akhmediev

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Variable Coefficients ◽

Nonlinear Schrodinger Equation ◽

Time Variable ◽

Integrable Equations ◽

Nonlinear Schrödinger

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Lie Symmetry Analysis of the Nonlinear Schrödinger Equation with Time Dependent Variable Coefficients

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-021-00953-3 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Preeti Devi ◽

K. Singh

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Variable Coefficients ◽

Lie Symmetry ◽

Nonlinear Schrodinger Equation ◽

Symmetry Analysis ◽

Time Dependent ◽

Lie Symmetry Analysis ◽

Nonlinear Schrödinger

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