Quasi-Periodic Solutions for Two Dimensional Generalized Boussinesq Equation with Higher Order Nonlinearity

• Yanling Shi ^[1]
  1. [1] Yancheng Institute of Technology

     Yancheng Institute of Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, two dimensional generalized Boussinesq equation utt − u + 2u + (u5) = 0, x ∈ T2, t ∈ R under periodic boundary conditions is considered. It is proved that the above equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional Hamiltonian system. The proof is based on an infinite dimensional KAM theorem, partial Birkhoff normal form and scaling skills.

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