Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation

摘要

In this paper, we consider the d-dimensional beam equation with convolution potential under periodic boundary conditions. We will apply the Kolmogorov-Arnold-Moser theorem in Eliasson and Kuksin [Ann. Math. 172, 371-435 (2010)] into this system and obtain that for sufficiently small epsilon, there is a large subset S' of S such that for all s is an element of S', the solution u of the unperturbed system persists as a time-quasiperiodic solution which has all Lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients. (C) 2015 AIP Publishing LLC.