KAM tori for a nonlinear beam equation with an almost periodic potential based on the space variable

• Published in: Communications in nonlinear science & numerical simulation Vol. 150; p. 109045
• Main Authors: Zhu, Sixue, Rui, Jie
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2025
• Subjects: Almost periodic solutions; Infinite-dimensional Hamiltonian systems; KAM theory; Nonlinear beam equations; Infinite-dimensional Hamiltonian systems; 11K70; Almost periodic solutions; 37K55; KAM theory; Nonlinear beam equations
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2025.109045

In this paper, we study a nonlinear beam equation subject to an almost periodic forced term, which is analytic on t and x. Under appropriate assumptions on the perturbation, we show the existence of almost periodic solutions of such an equation and present a more precise analytical solution. The proof is based on the partial normal form and infinite-dimensional KAM (Kolmogorov–Arnold–Moser) theory. •The final quartic normal form provides more detailed dynamic properties.•Solve a more complicated case where the forcing term involves dual variables ω and x.•The introduction of probability measures resolves the small divisor difficulty.