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