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On a hypercylicity criterion for strongly continuous semigroups
One dimensional Dirac equation with quadratic nonlinearities
1. | Department of Mathematics, Shimane University, Matsue 690-8504, Japan |
[1] |
Axel Grünrock, Sebastian Herr. The Fourier restriction norm method for the Zakharov-Kuznetsov equation. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2061-2068. doi: 10.3934/dcds.2014.34.2061 |
[2] |
Frédéric Bernicot, Vjekoslav Kovač. Sobolev norm estimates for a class of bilinear multipliers. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1305-1315. doi: 10.3934/cpaa.2014.13.1305 |
[3] |
Felipe Hernandez. A decomposition for the Schrödinger equation with applications to bilinear and multilinear estimates. Communications on Pure and Applied Analysis, 2018, 17 (2) : 627-646. doi: 10.3934/cpaa.2018034 |
[4] |
Jan-Cornelius Molnar. On two-sided estimates for the nonlinear Fourier transform of KdV. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3339-3356. doi: 10.3934/dcds.2016.36.3339 |
[5] |
Mégane Bournissou. Local controllability of the bilinear 1D Schrödinger equation with simultaneous estimates. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022027 |
[6] |
Juan H. Arredondo, Francisco J. Mendoza, Alfredo Reyes. On the norm continuity of the hk-fourier transform. Electronic Research Announcements, 2018, 25: 36-47. doi: 10.3934/era.2018.25.005 |
[7] |
Hartmut Pecher. Local well-posedness for the nonlinear Dirac equation in two space dimensions. Communications on Pure and Applied Analysis, 2014, 13 (2) : 673-685. doi: 10.3934/cpaa.2014.13.673 |
[8] |
Reika Fukuizumi, Louis Jeanjean. Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 121-136. doi: 10.3934/dcds.2008.21.121 |
[9] |
Nikolaos Bournaveas. Local well-posedness for a nonlinear dirac equation in spaces of almost critical dimension. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 605-616. doi: 10.3934/dcds.2008.20.605 |
[10] |
Hartmut Pecher. Corrigendum of "Local well-posedness for the nonlinear Dirac equation in two space dimensions". Communications on Pure and Applied Analysis, 2015, 14 (2) : 737-742. doi: 10.3934/cpaa.2015.14.737 |
[11] |
Dan-Andrei Geba, Evan Witz. Revisited bilinear Schrödinger estimates with applications to generalized Boussinesq equations. Electronic Research Archive, 2020, 28 (2) : 627-649. doi: 10.3934/era.2020033 |
[12] |
Maria J. Esteban, Eric Séré. An overview on linear and nonlinear Dirac equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 381-397. doi: 10.3934/dcds.2002.8.381 |
[13] |
J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao. Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm. Communications on Pure and Applied Analysis, 2003, 2 (1) : 33-50. doi: 10.3934/cpaa.2003.2.33 |
[14] |
Jiecheng Chen, Dashan Fan, Lijing Sun. Asymptotic estimates for unimodular Fourier multipliers on modulation spaces. Discrete and Continuous Dynamical Systems, 2012, 32 (2) : 467-485. doi: 10.3934/dcds.2012.32.467 |
[15] |
Jong-Shenq Guo, Bei Hu. Blowup rate estimates for the heat equation with a nonlinear gradient source term. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 927-937. doi: 10.3934/dcds.2008.20.927 |
[16] |
Benjamin Dodson. Improved almost Morawetz estimates for the cubic nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2011, 10 (1) : 127-140. doi: 10.3934/cpaa.2011.10.127 |
[17] |
Roberta Bosi, Jean Dolbeault, Maria J. Esteban. Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators. Communications on Pure and Applied Analysis, 2008, 7 (3) : 533-562. doi: 10.3934/cpaa.2008.7.533 |
[18] |
Thomas Bartsch, Tian Xu. Strongly localized semiclassical states for nonlinear Dirac equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 29-60. doi: 10.3934/dcds.2020297 |
[19] |
Xu Zhang. On the concentration of semiclassical states for nonlinear Dirac equations. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5389-5413. doi: 10.3934/dcds.2018238 |
[20] |
Xiaoyan Lin, Xianhua Tang. Solutions of nonlinear periodic Dirac equations with periodic potentials. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2051-2061. doi: 10.3934/dcdss.2019132 |
2021 Impact Factor: 1.588
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