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Global well-posedness and non-linear stability of periodic traveling waves for a Schrödinger-Benjamin-Ono system
1. | IME-USP, Department of Mathematics, Rua do Matão 1010, Cidade Universitária, CEP 05508-090, São Paulo, SP, Brazil |
2. | IMPA, Estrada Dona Castorina 110, CEP 22460-320 Rio de Janeiro, RJ, Brazil |
3. | UFRJ, Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, CEP: 21945-970, Rio de Janeiro, RJ |
[1] |
Linglong Du, Caixuan Ren. Pointwise wave behavior of the initial-boundary value problem for the nonlinear damped wave equation in $\mathbb{R}_{+}^{n} $. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3265-3280. doi: 10.3934/dcdsb.2018319 |
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Ronald Mickens, Kale Oyedeji. Traveling wave solutions to modified Burgers and diffusionless Fisher PDE's. Evolution Equations and Control Theory, 2019, 8 (1) : 139-147. doi: 10.3934/eect.2019008 |
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Hui Yang, Yuzhu Han. Initial boundary value problem for a strongly damped wave equation with a general nonlinearity. Evolution Equations and Control Theory, 2022, 11 (3) : 635-648. doi: 10.3934/eect.2021019 |
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Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems and Imaging, 2008, 2 (1) : 121-131. doi: 10.3934/ipi.2008.2.121 |
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Patricio Cerda, Leonelo Iturriaga, Sebastián Lorca, Pedro Ubilla. Positive radial solutions of a nonlinear boundary value problem. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1765-1783. doi: 10.3934/cpaa.2018084 |
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Runzhang Xu, Mingyou Zhang, Shaohua Chen, Yanbing Yang, Jihong Shen. The initial-boundary value problems for a class of sixth order nonlinear wave equation. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5631-5649. doi: 10.3934/dcds.2017244 |
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Ning-An Lai, Yi Zhou. Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1499-1510. doi: 10.3934/cpaa.2018072 |
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Zhaosheng Feng, Goong Chen. Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 763-780. doi: 10.3934/dcds.2009.24.763 |
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Hongqiu Chen, Jerry L. Bona. Periodic traveling--wave solutions of nonlinear dispersive evolution equations. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4841-4873. doi: 10.3934/dcds.2013.33.4841 |
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Anna Geyer, Ronald Quirchmayr. Traveling wave solutions of a highly nonlinear shallow water equation. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1567-1604. doi: 10.3934/dcds.2018065 |
[11] |
Cunming Liu, Jianli Liu. Stability of traveling wave solutions to Cauchy problem of diagnolizable quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4735-4749. doi: 10.3934/dcds.2014.34.4735 |
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Harunori Monobe, Hirokazu Ninomiya. Traveling wave solutions with convex domains for a free boundary problem. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 905-914. doi: 10.3934/dcds.2017037 |
[13] |
Chueh-Hsin Chang, Chiun-Chuan Chen, Chih-Chiang Huang. Traveling wave solutions of a free boundary problem with latent heat effect. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 1797-1809. doi: 10.3934/dcdsb.2021028 |
[14] |
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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J. Colliander, A. D. Ionescu, C. E. Kenig, Gigliola Staffilani. Weighted low-regularity solutions of the KP-I initial-value problem. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 219-258. doi: 10.3934/dcds.2008.20.219 |
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Tatsien Li, Libin Wang. Global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 59-78. doi: 10.3934/dcds.2005.12.59 |
[18] |
Vladimir V. Varlamov. On the initial boundary value problem for the damped Boussinesq equation. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 431-444. doi: 10.3934/dcds.1998.4.431 |
[19] |
Davide Bellandi. On the initial value problem for a class of discrete velocity models. Mathematical Biosciences & Engineering, 2017, 14 (1) : 31-43. doi: 10.3934/mbe.2017003 |
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John R. Graef, Lingju Kong, Bo Yang. Positive solutions of a nonlinear higher order boundary-value problem. Conference Publications, 2009, 2009 (Special) : 276-285. doi: 10.3934/proc.2009.2009.276 |
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