Quasi-periodic Solutions for Two Dimensional Modified Boussinesq Equation

In this paper, two dimensional modified Boussinesq equation u(tt)+Delta(2)u+Delta(u(3))=0, x is an element of T-2, t is an element of 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 and Birkhoff normal form.

Automated summary

This paper discusses the solutions of the two-dimensional modified Boussinesq equation under periodic boundary conditions, proving the existence of a specific class of solutions and providing a mathematical proof for it.