Quasi-periodic Solutions for a Generalized Higher-Order Boussinesq Equation.

In this paper one-dimensional generalized eighth-order Boussinesq equation u tt - ∂ x 2 u + β ∂ x 4 u - ∂ x 6 u + ∂ x 8 u + (u 3) xx = 0 , β = ± 1 <graphic href="12346_2023_840_Article_Equ25.gif"></graphic> with the boundary conditions u (0 , t) = u (π , t) = u xx (0 , t) = u xx (π , t) = u xxxx (0 , t) = u xxxx (π , t) = 0 is considered. It is proved that the above equation admits small-amplitude quasi-periodic solutions. The proof is based on an infinite dimensional KAM theorem and Birkhoff normal form. [ABSTRACT FROM AUTHOR]