Modified Scattering of Cubic Nonlinear Schr\"odinger Equation on Rescaled Waveguide Manifolds

Bobby Wilson; Xueying Yu

Modified Scattering of Cubic Nonlinear Schr\"odinger Equation on Rescaled Waveguide Manifolds

Analysis of PDEs 2022-07-18 v1

Authors: Bobby Wilson , Xueying Yu

Abstract

We use modified scattering theory to demonstrate that small-data solutions to the cubic nonlinear Schr\"odinger equation on rescaled waveguide manifolds, $\mathbb{R} \times \mathbb{T}^d$ for $d\geq 2$ , demonstrate boundedness of Sobolev norms as well as weak instability.

Keywords

modified scattering cubic nonlinear schrödinger equation rescaled waveguide manifolds sobolev norms weak instability

Cite

@article{arxiv.2207.07248,
  title  = {Modified Scattering of Cubic Nonlinear Schr\"odinger Equation on Rescaled Waveguide Manifolds},
  author = {Bobby Wilson and Xueying Yu},
  journal= {arXiv preprint arXiv:2207.07248},
  year   = {2022}
}

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