NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ℝd

DOI10.1080/00036811.2018.1544620zbMath1459.35342arXiv1710.07077OpenAlexW2900876603MaRDI QIDQ5147277

Tomáš Dohnal, Daniel Rudolf

Publication date: 3 February 2021

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.07077

zbMATH Keywords

solitary waveperiodic mediaBloch wavesnonlinear wave equationapproximation errorNLS approximationGross-Pitaevskiiwavepackets

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for discrete and fast Fourier transforms (65T50) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Soliton solutions (35C08) Second-order semilinear hyperbolic equations (35L71)

Related Items (2)

A quasilinear transmission problem with application to Maxwell equations with a divergence-free \(\mathcal{D} \)-field ⋮ Rigorous Envelope Approximation for Interface Wave Packets in Maxwell’s Equations with Two Dimensional Localization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions
• Diffractive optics with harmonic radiation in 2d nonlinear photonic crystal waveguide
• Justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear Schrödinger equation
• Photonic crystals. Mathematical analysis and numerical approximation.
• Justification of the nonlinear Schrödinger equation in spatially periodic media
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential
• Perturbation theory for linear operators.
• KP description of unidirectional long waves. The model case
• Structure of a quantized vortex in boson systems
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• Homogenization of Periodic Structures via Bloch Decomposition
• Validity and Limitation of the Newell‐Whitehead Equation
• Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
• Nonlinear propagation of light in one-dimensional periodic structures

This page was built for publication: NLS approximation for wavepackets in periodic cubically nonlinear wave problems in ℝ^d