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Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation
1. | Department of Applied Mathematics, Science University of Tokyo, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162 |
2. | Departamento de Ciencias Básicas, Instituto Tecnologico de Morelia, CP 58080, Morelia, Michoacan, Mexico |
3. | Instituto de Física y Matemáticas, Universidad Michoacana, AP 2-82, CP 58040, Morelia, Michoacana, Mexico |
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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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Nakao Hayashi, Pavel I. Naumkin. Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 383-400. doi: 10.3934/dcds.1997.3.383 |
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Razvan Mosincat, Haewon Yoon. Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 47-80. doi: 10.3934/dcds.2020003 |
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Meina Gao, Jianjun Liu. Quasi-periodic solutions for derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2101-2123. doi: 10.3934/dcds.2012.32.2101 |
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Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6943-6974. doi: 10.3934/dcds.2016102 |
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Kazumasa Fujiwara, Tohru Ozawa. On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation. Evolution Equations and Control Theory, 2018, 7 (2) : 275-280. doi: 10.3934/eect.2018013 |
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Phan Van Tin. On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions. Evolution Equations and Control Theory, 2022, 11 (3) : 837-867. doi: 10.3934/eect.2021028 |
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Zhaowei Lou, Jianguo Si, Shimin Wang. Invariant tori for the derivative nonlinear Schrödinger equation with nonlinear term depending on spatial variable. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022064 |
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Nakao Hayashi, Pavel Naumkin. On the reduction of the modified Benjamin-Ono equation to the cubic derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 237-255. doi: 10.3934/dcds.2002.8.237 |
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Zihua Guo, Yifei Wu. Global well-posedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 257-264. doi: 10.3934/dcds.2017010 |
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Minoru Murai, Kunimochi Sakamoto, Shoji Yotsutani. Representation formula for traveling waves to a derivative nonlinear Schrödinger equation with the periodic boundary condition. Conference Publications, 2015, 2015 (special) : 878-900. doi: 10.3934/proc.2015.0878 |
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Kelin Li, Huafei Di. On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4293-4320. doi: 10.3934/dcdss.2021122 |
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Thierry Cazenave, Yvan Martel, Lifeng Zhao. Finite-time blowup for a Schrödinger equation with nonlinear source term. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1171-1183. doi: 10.3934/dcds.2019050 |
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Jerry L. Bona, Laihan Luo. Large-time asymptotics of the generalized Benjamin-Ono-Burgers equation. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 15-50. doi: 10.3934/dcdss.2011.4.15 |
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Rolci Cipolatti, Otared Kavian. On a nonlinear Schrödinger equation modelling ultra-short laser pulses with a large noncompact global attractor. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 121-132. doi: 10.3934/dcds.2007.17.121 |
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Hideo Takaoka. Energy transfer model for the derivative nonlinear Schrödinger equations on the torus. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5819-5841. doi: 10.3934/dcds.2017253 |
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Nakao Hayashi, Pavel I. Naumkin, Patrick-Nicolas Pipolo. Smoothing effects for some derivative nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 685-695. doi: 10.3934/dcds.1999.5.685 |
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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 |
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Shaoming Guo, Xianfeng Ren, Baoxiang Wang. Local well-posedness for the derivative nonlinear Schrödinger equation with $ L^2 $-subcritical data. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4207-4253. doi: 10.3934/dcds.2021034 |
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