References
- Bourgain J. Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE. Int Math Res Not. 1994;11:475–497.
- Bourgain J. Construction of periodic solutions of nonlinear wave equations in higher dimension. Geom Funct Anal. 1995;5:629–639.
- Bourgain J. Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations. Ann Math. 1998;148:363–439.
- Bourgain J. Nonlinear Schrödinger equations. Providence: American Mathematical Society; 1999. (Park City Ser.; 5).
- Bourgain J. Green's function estimates for lattice Schrödinger operators and applications. Princeton: Princeton Univ. Press; 2005. (Annals of Mathematics Studies; 158.
- Craig W, Wayne CE. Newton's method and periodic solutions of nonlinear wave equations. Comm Pure Appl Math. 1993;46:1409–1498.
- Kuksin SB. Nearly integrable infinite-dimensional Hamiltonian systems. Berlin: Springer-Verlag; 1993. (Lecture Notes in Mathematics; 1556).
- Pöschel J. A KAM-theorem for some nonlinear partial differential equations. Ann Scuola Norm Sup Pisa Cl Sci. 1996;23:119–148.
- Wayne CE. Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory. Comm Math Phys. 1990;127:479–528.
- Kuksin SB. Hamiltonian perturbations of infinite-dimensional linear systems with imaginary spectrum. Funktsional Anal I Prilozhen. 1987;21:192–205.
- Bambusi D. Birkhoff normal form for some nonlinear PDEs. Comm Math Phys. 2003;234:253–285.
- Bambusi D, Berti M. A Birkhoff-Lewis-type theorem for some Hamiltonian PDEs. Siam J Math Anal. 2005;37:83–102.
- Eliasson LH, Kuksin SB. Four lectures on KAM for the non-linear Schrödinger equation. Hamiltonian Dyn Syst Appl Ser B. 2008;20:179–212.
- Eliasson LH, Kuksin SB. KAM for the nonlinear Schrödinger equation. Ann Math. 2010;172:371–435.
- Kuksin SB, Pöschel J. Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear schrödinger equation. Ann Math. 1996;143:149–179.
- Pöschel J. Quasi-periodic solutions for a nonlinear wave equation. Comment Math Helv. 1996;71:269–296.
- Shi Y, Xu J, Xu X. On quasi-periodic solutions for a generalized Boussinesq equation. Nonlinear Anal. 2014;105:50–61.
- Shi Y, Xu J, Xu X. Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing. Discrete Continuous Dyn Syst B. 2017;22:2501–2519.
- Shi Y, Lu X, Xu J, et al. Quasi-periodic solutions for Schrödinger equation with derivative nonlinearity. Dyn Syst. 2015;30:158–188.
- Chierchia L, You J. KAM tori for 1D nonlinear wave equations with periodic boundary conditions. Comm Math Phys. 2000;211:497–525.
- Geng J, You J. A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions. J Differ Equ. 2005;209:1–56.
- Geng J, You J. A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces. Comm Math Phys. 2006;262:343–372.
- Chen, Y., Geng J. A KAM theorem for higher dimensional wave equations under nonlocal perturbation. J Dyn Differ Equ. 2020;32:419–440.
- Baldi P, Berti M, Montalto R. KAM for autonomous quasi-linear perturbations of KdV. Ann Inst H Poincare Anal Non Lineaire. 2016;33:1589–1638.
- Kappeler T, Poschel J. KdV & KAM. Vol. 45. Berlin: Springer-Verlag; 2003.
- Liu J, Yuan X. A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations. Comm Math Phys. 2011;307:629–673.
- Zhang J, Gao M, Yuan X. KAM tori for reversible partial differential equations. Nonlinearity. 2011;24:1189–1228.
- Zhou S. An abstract infinite dimensional KAM theorem with application to nonlinear higher dimensional Schrödinger equation systems, arXiv preprint: arxiv:1701.05727v1.
- Grebert B, Rocha V. Stable and unstable time quasi periodic solutions for a system of coupled NLS equations, arXiv preprint: arxiv.1710.09173v1.
- Geng J, You J. KAM tori for higher dimensional beam equations with constant potentials. Nonlinearity. 2006;19:2405–2423.
- Bambusi D. On long time stability in Hamiltonian perturbations of non-resonant linear PDEs. Nonlinearity. 1999;12:823–850.