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Mathematics > Numerical Analysis

arXiv:1805.02468 (math)
[Submitted on 7 May 2018 (v1), last revised 6 Nov 2018 (this version, v2)]

Title:Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schr{ö}dinger equations on $h\mathbb{Z}$

Authors:Joackim Bernier (MINGUS)
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Abstract:We consider the discrete nonlinear Schr{ö}dinger equations on a one dimensional lattice of mesh h, with a cubic focusing or defocusing nonlinearity. We prove a polynomial bound on the growth of the discrete Sobolev norms, uniformly with respect to the stepsize of the grid. This bound is based on a construction of higher modified energies.
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
Cite as: arXiv:1805.02468 [math.NA]
  (or arXiv:1805.02468v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1805.02468

Submission history

From: Joackim Bernier [view email] [via CCSD proxy]
[v1] Mon, 7 May 2018 12:20:32 UTC (15 KB)
[v2] Tue, 6 Nov 2018 12:05:23 UTC (16 KB)
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