Birkhoff normal forms for the wave equations with nonlinear terms depending on the time and space variables

Yi Wang

COMPUTER MODELLING & NEW TECHNOLOGIES 2014 18(4) 42-49

School of Mathematics and Quantitative Economic, Shandong University of Finance and Economics, Jinan, Shandong 250014, P. R. China

The one-dimensional (1D) quasi-periodically forced nonlinear wave equation with periodic boundary conditions is considered. It is proved that there is a real analytic and symplectic change of coordinates, which can transform the Hamiltonian to the Birkhoff normal form.