Lindstedt series solutions of the Fermi-Pasta-Ulam lattice
نویسندگان
چکیده
منابع مشابه
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 ǫ as the expansion parameter, where ǫ is the coefficient of the quartic coupling between nearest neighbors. We compare our non-secular perturbative solutions to numerical solutions and find striking agree...
متن کاملTHE FERMI-PASTA-ULAM LATTICE Background The Fermi-Pasta-Ulam lattice is named after the experiments
The Fermi-Pasta-Ulam lattice is named after the experiments performed by Enrico Fermi, John Pasta, and Stanislaw Ulam in 1954-5 on the Los Alamos MANIAC computer, one of the first electronic computers. As reported in Ulam’s autobiography [Uh], Fermi immediately suggested using the new machine for theoretical work, and it was decided to start by studying the vibrations of a string under the infl...
متن کاملThe Fermi-Pasta-Ulam problem(∗)
The Fermi-Pasta-Ulam model is a system of N+2 equal particles on a line with mutual interactions between adjacent particles, provided by a potential of the form V (r) = r/2 + αr/3 + βr/4; certain boundary conditions are also assigned, typically with the two extreme particles fixed. For α = β = 0 the system is a linear one, and by a familiar linear transformation it can be reduced to a system of...
متن کاملSymmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
The Fermi-Pasta-Ulam (FPU) lattice with periodic boundary conditions and n particles admits a large group of discrete symmetries. The fixed point sets of these symmetries naturally form invariant symplectic manifolds that are investigated in this short note. For each k dividing n we find k degree of freedom invariant manifolds. They represent short wavelength solutions composed of k Fourier-mod...
متن کاملAn integrable approximation for the Fermi-Pasta-Ulam lattice
This contribution presents a review of results obtained from computations of approximate equations of motion for the Fermi-Pasta-Ulam lattice. These approximate equations are obtained as a finite-dimensional Birkhoff normal form. It turns out that in many cases, the Birkhoff normal form is suitable for application of the KAM theorem. In particular this proves Nishida’s 1971 conjecture stating t...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2721346