An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation |
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Authors: | Jiansheng Geng Xindong Xu Jiangong You |
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Institution: | Department of Mathematics and Institute of Mathematical Science, Nanjing University, Nanjing 210093, PR China |
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Abstract: | We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the two dimensional nonlinear Schrödinger equation with periodic boundary conditions. We obtain for the equation a Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. |
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Keywords: | MSC: 37K55 35B10 |
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