A Nekhoroshev type theorem for nonlinear Schrödinger equation on the \(d\)-dimensional torus. (English) Zbl 07898654
Summary: In this paper, we study the long time dynamical behavior of the solutions for \(d\)-dimensional nonlinear Schrödinger equation on the torus \(\mathbb{T}^d\). Precisely, by using Birkhoff normal form technique, we prove the subexponential long time stability of solutions with small initial data in Gevrey space.
MSC:
| 37K55 | Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 35B35 | Stability in context of PDEs |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
Keywords:
\(d\)-dimensional nonlinear Schrödinger equation; Nekhoroshev-type theorem; subexponential long time stabilityReferences:
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