KAM tori for the generalized Bejamin-Bona-Mahony equation

TL;DR

This paper proves the existence of numerous time-quasi-periodic solutions for the generalized Benjamin-Bona-Mahony equation using a novel infinite-dimensional KAM theorem, advancing understanding of nonlinear wave equations.

Contribution

It introduces a new infinite-dimensional KAM theorem applicable to the gBBM equation with finite limit-point frequencies, demonstrating the existence of quasi-periodic solutions.

Findings

Existence of many time-quasi-periodic solutions for gBBM.

Application of a new KAM theorem with finite limit-points.

Advancement in understanding nonlinear wave dynamics.

Abstract

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