References
- Davey A, Stewartson K. On 3-dimensional packets of surface waves. Proc R Soc Lond A. 1974;338:101–110.
- Ghidaglia J-M, Saut JC. On the initial value problem for the Davey–Stewartson systems. Nonlinearity. 1990;3:475–506.
- Guo B, Wang B. The Cauchy problem for Davey–Stewartson systems. Commun Pure Appl Math. 1999;LII:1477–1490.
- Tsutsumi M. Decay of weak solution to the Davey–Stewartson systems. J Math Anal Appl. 1994;182(3):259–349.
- Ozawa T. Exact blow-up solution to the Cauchy problem for the Davey–Stewartson system. Proc R Soc Lond A. 1992;436(1897):345–349.
- Ohta M. Instability of standing waves for the generalized Davey–Stewartson system. Ann l'I. H. P. Section A. 1995;62:69–80.
- Ohta M. Stability of standing waves for the generalized Davey–Stewartson system. J Dyn Differ Equ. 1994;6:325–334.
- Gan Z, Zhang J. Sharp threshold of global existence and instability of standing wave for a Davey–Stewartson system. Commun Math Phys. 2008;283:93–125.
- Nishinari K, Abe K, Satsuma J. Multidimensional behavior of an electrostatic ion wave in a magnetized plasma. Phys Plasmas. 1994;1:2559–2565.
- Zakharov V, Schulman E. Integrability of nonlinear systems and perturbation theory. In: Zakharov, editor. What is integrability? Springer-Verlag; 1991. p. 189–250. (Springer series on nonlinear dynamics).
- Lu J, Wu Y. Sharp threshold for scattering of a generalized Davey–Stewartson system in three dimension. Commun Pure Appl Anal. 2015;14(5):1641–1670.
- Lu J, Tang X. Energy scattering of a generalized Davey–Stewartson system in three dimension. Acta Math Sin Engl Ser. 2017;33(9):1206–1224.
- Sulem C, Sulem P-L. The nonlinear Schrödinger equation, self-focusing and wave collapse. New York (NY): Springer-Verlag; 1999.
- Tao T, Visan M, Zhang X. The nonlinear Schrödinger equation with combined power-type nonlinearities. Commun Partial Differ Equ. 2007;32:1281–1343.
- Colliander J, Keel M, Staffilani G, et al. Global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in R3. Ann Math. 2007;166:1–100.
- Miao C, Xu G, Zhao L. The dynamics of the 3D radial NLS with the combined terms. Commun Math Phys. 2013;318(3):767–808.
- Miao C, Xu G, Zhao L. The dynamics of the NLS with the combined terms in five and higher dimensions. In: Some topics in harmonic analysis and applications. Beijing and USA: Higher Education Press and International Press; 2015. p. 265–298. (Advanced lectures in mathematics; ALM34).
- Lu J, Xia S. The dynamics of the 3D NLS with the convolution term. Math Methods Appl Sci. 2015;38:3097–3117.
- Fang D, Han Z, Dai J. The nonlinear Schrödinger equations with the combined nonlinearities of power-type and Hartree-type. Chin Ann Math Ser B. 2011;32:435–474.
- Miao C, Xu G, Zhao L. Global well-posedness and scattering for the energy-critical, defusing Hartree equation for radial data. J Funct Anal. 2007;253:605–627.
- Miao C, Xu G, Zhao L. Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case. Coll Math. 2009;114:213–236.
- Miao C, Xu G, Zhao L. Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data. J Funct Anal. 2007;253:605–627.
- Miao C, Xu G, Zhao L. Global well-posedness and scattering for the defocusing H12-subcritical Hartree equation in Rd. Ann I H Poincaré-NA. 2009;26:1831–1852.
- Miao C, Xu G, Zhao L. Global well-posedness and scattering for the mass-critical Hartree equation with radial data. J Math Pures Appl. 2009;91:49–79.
- Miao C, Xu G, Zhao L. Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in R1+n. Commun Partial Differ Equ. 2011;36:729–776.
- Kenig CK, Merle F. Global well-posedness, scattering, and blow-up for the energy-critical focusing nonlinear Schrödinger equation in the radial case. Invent Math. 2006;166:645–675.
- Cazenave T. Semilinear Schrödinger equations. New York (NY): New York University Courant Institute of Mathematical Sciences; 2003. 84–93. (Courant lecture notes in mathematics; vol. 10).
- Keel M, Tao T. Endpoint Strichartz estimates. Am J Math. 1998;120(5):955–980.
- Tao T. Nonlinear dispersive equations, local and global analysis. Published for the Conference Board of the Mathematical Science, Washington, DC; Providence, RI: American Mathematical Society; 2006. p. 73–82. (CBMS. Regional conference Series in Mathematics; 106).
- Foschi D. Inhomogeneous Strichartz estimates. J Hyperbolic Differ Equ. 2005;2:1–24.
- Cipolatti R. On the existence of standing waves for a Davey–Stewartson system. Commun Partial Differ Equ. 1992;17:967–988.
- Cipolatti R. On the instability of ground states for a Davey–Stewartson system. Ann l'I. H. P. Section A. 1993;58(1):85–104.
- Talenti G. Best constant in Sobolev inequality. Ann Mat Pura Appl. 1976;110:353–372.
- Killip R, Visan M. The focusing energy-critical Schrödinger equation in dimensions five and higher. Am J Math. 2010;132(2):361–424.
- Lu J. Dynamics of modified Davey–Stewartson system in R3. Coll Math. 2016;145(1):1–19.
- Ibrahim S, Masmoudi N, Nakanishi K. Scattering threshold for the focusing nonlinear Klein–Gordon equation. Anal & PDE. 2011;4(3):405–460.
- Duyckaerts T, Holmer J, Roudenko S. Scattering for the non-radial 3D cubic nonlinear Schrödinger equation. Math Res Lett. 2008;15:1233–1250.