Lindstedt Series Solutions of the Fermi-Pasta-Ulam Lattice

Details Lindstedt Series Solutions of the Fermi-Pasta-Ulam Lattice Lindstedt Series Solutions of the Fermi-Pasta-Ulam Lattice

2007-03-12

arxiv.org/abs/math-ph/0703037v1

J. Math. Phys., 48, 052702 (2007)

Physics

Mathematical Physics

17 pages, 10 figures. To appear in the Journal of Mathematical Physics

Scientific paper

10.1063/1.2721346

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.

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