Quasi-periodic solutions for the generalized Benjamin–Bona–Mahony​ equation

Abstract

A generalized Benjamin–Bona–Mahony (gBBM) equation ut−uxxt+ux+u4ux=0,subject to the periodic boundary condition is studied in this paper. Based on a new infinite dimensional Kolmogorov–Arnold–Moser (KAM) theorem with normal frequencies of finite limit-points, it is shown that the above gBBM equation admits plenty of time-quasi-periodic solutions with two frequencies of high modes.