KAM Tori for Completely Resonant Hamiltonian Derivative Beam Equations on T2

KAM Tori for Completely Resonant Hamiltonian Derivative Beam Equations on T2

In this paper, we study a class of completely resonant beam equations with derivative nonlinearities on T 2 u tt + Δ 2 u + u | ∇ u | 2 + u 2 Δ u = 0 . We will prove the existence of small-amplitude, quasi-periodic solutions for the above equations via KAM method.

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Veröffentlicht in:Journal of dynamics and differential equations 2021, Vol.33 (1), p.525-547
Hauptverfasser: Ge, Chuanfang, Geng, Jiansheng, Lou, Zhaowei
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Toruses
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Zusammenfassung:In this paper, we study a class of completely resonant beam equations with derivative nonlinearities on T 2 u tt + Δ 2 u + u | ∇ u | 2 + u 2 Δ u = 0 . We will prove the existence of small-amplitude, quasi-periodic solutions for the above equations via KAM method.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-019-09819-1