This paper is concerned with the existence of families of time-periodic solutions for the nonlinear wave equations with Hamiltonian perturbations on one-dimensional tori. We obtain the result by a new method: a para-differential conjugation together with a classical iteration scheme, which have been used for the nonlinear Schrödinger equation in . Avoiding the use of KAM theorem and Nash-Moser iteration method, though a para-differential conjugation, an equivalent form of the investigated nonlinear wave equations can be obtained, while the frequencies are fixed in a Cantor-like set whose complement has small measure. Applying the non-resonant conditions on each finite-dimensional subspaces, solutions can be constructed to the block diagonal equation on the finite subspace by a classical iteration scheme.
"Construction of Periodic Solutions for Nonlinear Wave Equations by a Para-differential Method." Taiwanese J. Math. 21 (5) 1057 - 1097, October, 2017. https://doi.org/10.11650/tjm/7914