Exact global control of small divisors in rational normal form. (English) Zbl 07867523
Summary: Rational normal form is a powerful tool to deal with Hamiltonian partial differential equations without external parameters. In this paper, we build rational normal form with exact global control of small divisors. As an application to nonlinear Schrödinger equations in Gevrey spaces, we prove sub-exponentially long time stability results for generic small initial data.
{© 2024 IOP Publishing Ltd & London Mathematical Society}
{© 2024 IOP Publishing Ltd & London Mathematical Society}
MSC:
| 37K55 | Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K45 | Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
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