Existence and Stability of Traveling Waves for Discrete Nonlinear Schrödinger Equations Over Long Times

DOI10.1137/18M1186484zbMath1417.65149arXiv1805.03578MaRDI QIDQ4633492

Erwan Faou, Joackim Bernier

Publication date: 3 May 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.03578

zbMATH Keywords

solitary wavesfinite differencesdiscrete nonlinear Schrödinger equationcontinuous limit

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items (4)

Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on \( h\mathbb{Z}\) ⋮ Growth of Sobolev norms and strong convergence for the discrete nonlinear Schrödinger equation ⋮ Continuous limits of linear and nonlinear quantum walks ⋮ On the continuum limit for the discrete nonlinear Schrödinger equation on a large finite cubic lattice

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