  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.
