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Modified wave operators for the Hartree equation with data, image and convergence in the same space
1. | Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan |
[1] |
Jean Ginibre, Giorgio Velo. Modified wave operators without loss of regularity for some long range Hartree equations. II. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1357-1376. doi: 10.3934/cpaa.2015.14.1357 |
[2] |
Kimitoshi Tsutaya. Scattering theory for the wave equation of a Hartree type in three space dimensions. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2261-2281. doi: 10.3934/dcds.2014.34.2261 |
[3] |
Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa. On small data scattering of Hartree equations with short-range interaction. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1809-1823. doi: 10.3934/cpaa.2016016 |
[4] |
Ricardo Weder, Dimitri Yafaev. Inverse scattering at a fixed energy for long-range potentials. Inverse Problems and Imaging, 2007, 1 (1) : 217-224. doi: 10.3934/ipi.2007.1.217 |
[5] |
Tarek Saanouni. Energy scattering for the focusing fractional generalized Hartree equation. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3637-3654. doi: 10.3934/cpaa.2021124 |
[6] |
Jason Murphy, Kenji Nakanishi. Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1507-1517. doi: 10.3934/dcds.2020328 |
[7] |
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 |
[8] |
Kirill D. Cherednichenko, Alexander V. Kiselev, Luis O. Silva. Functional model for extensions of symmetric operators and applications to scattering theory. Networks and Heterogeneous Media, 2018, 13 (2) : 191-215. doi: 10.3934/nhm.2018009 |
[9] |
Alexei Rybkin. On the boundary control approach to inverse spectral and scattering theory for Schrödinger operators. Inverse Problems and Imaging, 2009, 3 (1) : 139-149. doi: 10.3934/ipi.2009.3.139 |
[10] |
Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa. Corrigendum to "On small data scattering of Hartree equations with short-range interaction" [Comm. Pure. Appl. Anal., 15 (2016), 1809-1823]. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1939-1940. doi: 10.3934/cpaa.2017094 |
[11] |
Yang Liu, Wenke Li. A family of potential wells for a wave equation. Electronic Research Archive, 2020, 28 (2) : 807-820. doi: 10.3934/era.2020041 |
[12] |
Guangcun Lu. Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1243-1316. doi: 10.3934/dcds.2021154 |
[13] |
Peter Bates, Chunlei Zhang. Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 235-252. doi: 10.3934/dcds.2006.16.235 |
[14] |
Toshiyuki Suzuki. Scattering theory for semilinear Schrödinger equations with an inverse-square potential via energy methods. Evolution Equations and Control Theory, 2019, 8 (2) : 447-471. doi: 10.3934/eect.2019022 |
[15] |
Changxing Miao, Jiqiang Zheng. Scattering theory for energy-supercritical Klein-Gordon equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2073-2094. doi: 10.3934/dcdss.2016085 |
[16] |
Yaiza Canzani, A. Rod Gover, Dmitry Jakobson, Raphaël Ponge. Nullspaces of conformally invariant operators. Applications to $\boldsymbol{Q_k}$-curvature. Electronic Research Announcements, 2013, 20: 43-50. doi: 10.3934/era.2013.20.43 |
[17] |
H. A. Erbay, S. Erbay, A. Erkip. The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6101-6116. doi: 10.3934/dcds.2016066 |
[18] |
Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh. $L^p$ Estimates for the wave equation with the inverse-square potential. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 427-442. doi: 10.3934/dcds.2003.9.427 |
[19] |
Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh. Dispersive estimate for the wave equation with the inverse-square potential. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1387-1400. doi: 10.3934/dcds.2003.9.1387 |
[20] |
Changhun Yang. Scattering results for Dirac Hartree-type equations with small initial data. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1711-1734. doi: 10.3934/cpaa.2019081 |
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