Open AccessQuasi-periodic travelling waves for beam equations with damping on 3-dimensional rectangular tori
Author(s) -
Bochao Chen,
Yixian Gao
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021075
Subject(s) - torus , traveling wave , quasi periodic , mathematical analysis , mathematics , beam (structure) , periodic wave , amplitude , physics , quadrant (abdomen) , geometry , optics , astrophysics , medicine , pathology
This paper concerns the mathematical analysis of quasi-periodic travelling wave solutions for beam equations with damping on 3-dimensional rectangular tori. Provided that the generators of the rectangular torus satisfy certain relationships, by excluding some values of two model parameters, we establish the existence of small amplitude quasi-periodic travelling wave solutions with three frequencies. Moreover, it can be shown that such solutions are either continuations of rotating wave solutions, or continuations of quasi-periodic travelling wave solutions with two frequencies, and that the set of two model parameters is dense in the positive quadrant.