具有一般非线性的广义Boussinesq方程的概周期解  

Almost Periodic Solutions of the Generalized Boussinesq Equations with General Nonlinearities

作　　者：汪崧 

机构地区：[1]南京航空航天大学数学学院,江苏 南京

出　　处：《应用数学进展》2024年第11期5073-5088,共16页Advances in Applied Mathematics

摘　　要：本文考虑了一类在铰接边界条件下具有一般非线性的广义Boussinesq方程。利用无限维KAM (Kolmogorov-Arnold-Moser)理论,我们证明了在足够小的扰动下,这类方程存在无限多个小振幅、实解析且线性稳定的概周期解。This paper considers a class of generalized Boussinesq equations with general nonlinearities under hinged boundary conditions. Using infinite-dimensional KAM (Kolmogorov-Arnold-Moser) theory, we prove that for sufficiently small perturbations, the equations admit infinitely many of small amplitude, real analytic and linearly stable almost periodic solutions.

关 键 词：概周期解 广义BOUSSINESQ方程 KAM 

分 类 号：O17[理学—数学]