Pith. sign in

REVIEW 1 cited by

The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2003.08849 v2 pith:EAMFIR3O submitted 2020-03-19 math.AP math-phmath.MP

Benjamin Dodson , Avraham Soffer , Thomas Spencer This is my paper · ORCID
classification math.APmath-phmath.MP
keywords databoundedinitialequationexamplesexistencelocalnonlinear
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We study the nonlinear Schr\"odinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On the lattice we prove that solutions are polynomially bounded in time for any bounded data. In the continuum, local existence is proved for real analytic data by a Newton iteration scheme. Global existence for NLS with a regularized nonlinearity follows by analyzing a local energy norm.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Infinite energy quasi-periodic solutions to nonlinear Schr\"odinger equations on $\mathbb R$

    math.AP 2019-08 conditional novelty 8.0 of 10

    For non-integrable NLS on R, the paper proves existence of space-time quasi-periodic, infinite-energy, smooth solutions with two frequencies for a large Cantor set of parameters.

Pith tools