Lindstedt Series Solutions of the Fermi-Pasta-Ulam Lattice

We apply the Lindstedt method to the one dimensional Fermi-Pasta-Ulam $\beta$ lattice to find fully general solutions to the complete set of equations of motion. The pertubative scheme employed uses $\epsilon$ as the expansion parameter, where $\epsilon$ is the coefficient of the quartic coupling between nearest neighbors. We compare our non-secular perturbative solutions to numerical solutions and find striking agreement.