Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis

Ken Umeno

doi:10.1016/0167-2789(96)88314-x

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Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis

Ken Umeno

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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 Lamé equations. We also introduce the classification problem towards non-homogeneous nonlinear lattices including FPU lattices using non-integrability preserving transformation.

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BibTeX RIS

Ken Umeno. 1996-04-02. Non-perturbative non-integrability of non-homogeneous nonlinear lattices induced by non-resonance hypothesis. https://doi.org/10.1016/0167-2789(96)88314-x

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