Quasi-periodic Solutions for Two Dimensional Modified Boussinesq Equation
Quasi-periodic Solutions for Two Dimensional Modified Boussinesq Equation
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二维修正Boussinesq方程的准周期解
DOI：
10.1007/s10884-020-09829-4
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发表时间：
2021
影响因子：
1.3
通讯作者：
Junxiang Xu
中科院分区：
文献类型：
--
作者：
Yanling Shi;Junxiang Xu
本文考虑二维修正Boussinesq方程u（tt）+Delta（2）u+Delta（u（3））=0，x是T-2中的元素，t是R中的元素，在周期边界条件下.证明了上述方程存在Whitney光滑族的小振幅拟周期解，其对应于相应的无穷维Hamilton系统的有限维不变环面.证明是基于无限维KAM定理和Birkhoff标准形。
In this paper, two dimensional modified Boussinesq equation .u(tt)+Delta(2)u+Delta(u(3))=0, x is an element of T-2, t is an element of R .under periodic boundary conditions is considered. It is proved that the above equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional Hamiltonian system. The proof is based on an infinite dimensional KAM theorem and Birkhoff normal form.