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The nonlinear Schrödinger equation as a resonant normal form
1. | Dipartimento di Matematica “F. Enriques”, Universita di Milano, Via Saldini 50, 20133 Milano |
2. | Dipartimento di Matematica, Università degli studi di Milano, Via Saldini 50, 20133 Milano |
3. | Dipartimento di Fisica "Galileo Galilei", Università di Padova, Via Marzolo 8, 35131 Padova, Italy |
[1] |
F. Catoire, W. M. Wang. Bounds on Sobolev norms for the defocusing nonlinear Schrödinger equation on general flat tori. Communications on Pure and Applied Analysis, 2010, 9 (2) : 483-491. doi: 10.3934/cpaa.2010.9.483 |
[2] |
D.G. deFigueiredo, Yanheng Ding. Solutions of a nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 563-584. doi: 10.3934/dcds.2002.8.563 |
[3] |
Jaeyoung Byeon, Louis Jeanjean. Multi-peak standing waves for nonlinear Schrödinger equations with a general nonlinearity. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 255-269. doi: 10.3934/dcds.2007.19.255 |
[4] |
Thomas Duyckaerts, Carlos E. Kenig, Frank Merle. Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1275-1326. doi: 10.3934/cpaa.2015.14.1275 |
[5] |
Alessio Pomponio, Simone Secchi. A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities. Communications on Pure and Applied Analysis, 2010, 9 (3) : 741-750. doi: 10.3934/cpaa.2010.9.741 |
[6] |
Pavel I. Naumkin, Isahi Sánchez-Suárez. On the critical nongauge invariant nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 807-834. doi: 10.3934/dcds.2011.30.807 |
[7] |
Tarek Saanouni. Remarks on the damped nonlinear Schrödinger equation. Evolution Equations and Control Theory, 2020, 9 (3) : 721-732. doi: 10.3934/eect.2020030 |
[8] |
Younghun Hong. Scattering for a nonlinear Schrödinger equation with a potential. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1571-1601. doi: 10.3934/cpaa.2016003 |
[9] |
Alexander Komech, Elena Kopylova, David Stuart. On asymptotic stability of solitons in a nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1063-1079. doi: 10.3934/cpaa.2012.11.1063 |
[10] |
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 |
[11] |
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. Networks and Heterogeneous Media, 2021, 16 (2) : 283-315. doi: 10.3934/nhm.2021007 |
[12] |
Haidong Liu, Leiga Zhao. Existence results for quasilinear Schrödinger equations with a general nonlinearity. Communications on Pure and Applied Analysis, 2020, 19 (6) : 3429-3444. doi: 10.3934/cpaa.2020059 |
[13] |
Noboru Okazawa, Toshiyuki Suzuki, Tomomi Yokota. Energy methods for abstract nonlinear Schrödinger equations. Evolution Equations and Control Theory, 2012, 1 (2) : 337-354. doi: 10.3934/eect.2012.1.337 |
[14] |
Chenjie Fan, Zehua Zhao. Decay estimates for nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 3973-3984. doi: 10.3934/dcds.2021024 |
[15] |
Alexander Pankov. Nonlinear Schrödinger Equations on Periodic Metric Graphs. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 697-714. doi: 10.3934/dcds.2018030 |
[16] |
Nobu Kishimoto. A remark on norm inflation for nonlinear Schrödinger equations. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1375-1402. doi: 10.3934/cpaa.2019067 |
[17] |
Guoyuan Chen, Youquan Zheng. Concentration phenomenon for fractional nonlinear Schrödinger equations. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2359-2376. doi: 10.3934/cpaa.2014.13.2359 |
[18] |
Yohei Yamazaki. Transverse instability for a system of nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (2) : 565-588. doi: 10.3934/dcdsb.2014.19.565 |
[19] |
Paolo Antonelli, Daniel Marahrens, Christof Sparber. On the Cauchy problem for nonlinear Schrödinger equations with rotation. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 703-715. doi: 10.3934/dcds.2012.32.703 |
[20] |
Mohamad Darwich. On the $L^2$-critical nonlinear Schrödinger Equation with a nonlinear damping. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2377-2394. doi: 10.3934/cpaa.2014.13.2377 |
2020 Impact Factor: 1.327
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