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Mathematics > Numerical Analysis

arXiv:1805.03578 (math)
[Submitted on 9 May 2018]

Title:Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times

Authors:Joackim Bernier (IRMAR), Erwan Faou (IRMAR)
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Abstract:We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous this http URL construct a family of solutions close to the continuous traveling waves and prove their stability over long times. Applying a modulation method, we also show that we can describe the dynamics near these discrete traveling waves over long times.
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
Cite as: arXiv:1805.03578 [math.NA]
  (or arXiv:1805.03578v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1805.03578

Submission history

From: Erwan Faou [view email] [via CCSD proxy]
[v1] Wed, 9 May 2018 15:09:28 UTC (45 KB)
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