A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions

By Jiansheng Geng, Jiangong You. 2005

98 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7979170abcbb8e51775c2131ceedf82f2f979dec

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

1. Xindong Xu
2. Jiansheng Geng
3. Jiangong You
4. Y. Yi
5. Massimiliano Berti
6. Michela Procesi
7. P. Bolle
8. C. Procesi

In Statistical and Nonlinear Physics

1. Jiansheng Geng
2. Y. Yi
3. Xindong Xu
4. Jiangong You
5. Yuecai Han
6. Yong Li
7. Massimiliano Berti
8. Michela Procesi

Citations in the corpus

• A KAM Theorem for Hamiltonian Partial Differential Equations in Higher Dimensional Spaces (2006, methodology): “Hence compared with the normal form in [ 13 ], here the normal form N+ is simpler”
• Degenerate Lower Dimensional Tori in Hamiltonian Systems (2006, background): “M is non-singular over O), and also in infinite dimensional setting (see [3, 4, 5, 6, 7, 9, 11, 12, 14, 15, 16, 17, 19, 21, 28, 29, 30, 31, 33, 35, 36] and references therein).”
• Quasi-periodic solutions in a nonlinear Schrödinger equation (2007, unknown): “By taking advantage of the special form of the nonlinearity, the normal form will be derived using arguments of Liang and You [22] for eliminating lower-order, non-integrable terms.”
• An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation (2011, methodology): “There have been many remarkable results in KAM (Kolmogorov–Arnold–Moser) theory of Hamiltonian PDEs achieved either by methods from the finite dimensional KAM theory [1,8, 10,11,13–15,12,16–26,28], or by a Newtonian scheme developed by Craig, Wayne, Bourgain [4, 3,5,7,6,2,9].”