Quasi-Periodic Solutions of Nonlinear Wave Equations on the $d$-Dimensional Torus
Quasi-Periodic Solutions of Nonlinear Wave Equations on the $d$-Dimensional Torus
The main result of this research Monograph is the existence of small amplitude time quasi-periodic solutions for autonomous nonlinear wave equations $$ u_{tt} - \Delta u + V(x) u + g(x, u) = 0 \, , \quad x \in T^d \, , \quad g (x,u) = a(x) u^3 + O(u^4 …