dorsal/arxiv
View SchemaNon-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis
| Authors | Ken Umeno |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9603012 |
| URL | https://arxiv.org/abs/solv-int/9603012 |
| DOI | 10.1016/0167-2789(96)88314-X |
| Journal | Physica D94(1996)116-134. |
Abstract
We prove the non-integrability (non-existence of additional analytic conserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU) lattices by virtue of Lyapunov-Kovalevskaya- -Ziglin-Yoshida's monodromy method about the variational equations. The key to this analysis is that the normal variational equations along a certain solution happen to be in a type of Lam\'e equations. We also introduce the classification problem towards non-homogeneous nonlinear lattices including FPU lattices using non-integrability preserving transformation.
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"abstract": "We prove the non-integrability (non-existence of additional analytic\nconserved quantities other than Hamiltonian) for Fermi-Pasta-Ulam (FPU)\nlattices by virtue of Lyapunov-Kovalevskaya- -Ziglin-Yoshida\u0027s monodromy method\nabout the variational equations. The key to this analysis is that the normal\nvariational equations along a certain solution happen to be in a type of Lam\\\u0027e\nequations. We also introduce the classification problem towards non-homogeneous\nnonlinear lattices including FPU lattices using non-integrability preserving\ntransformation.",
"arxiv_id": "solv-int/9603012",
"authors": [
"Ken Umeno"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/0167-2789(96)88314-X",
"journal_ref": "Physica D94(1996)116-134.",
"title": "Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis",
"url": "https://arxiv.org/abs/solv-int/9603012"
},
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