Sobolev norms of $L^2$-solutions to NLS

Roman V. Bessonov; Sergey A. Denisov

doi:10.2140/pjm.2024.331.217

Sobolev norms of $L^2$-solutions to NLS

Analysis of PDEs 2024-11-06 v1 Mathematical Physics math.MP Spectral Theory

Authors: Roman V. Bessonov , Sergey A. Denisov

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Abstract

We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrodinger equation. For initial datum $q_0\in L^2(\mathbb{R})$ and $s\in [-1,0]$ , we prove that there exists a conserved quantity that is equivalent to $H^s(\mathbb{R})$ -norm of the solution.

Keywords

inverse spectral theory nonlinear Schrodinger equation Sobolev norms conserved quantity L^2 initial data

Cite

@article{arxiv.2211.07051,
  title  = {Sobolev norms of $L^2$-solutions to NLS},
  author = {Roman V. Bessonov and Sergey A. Denisov},
  journal= {arXiv preprint arXiv:2211.07051},
  year   = {2024}
}

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