A note on the validity of the Schrödinger approximation for the Helmholtz equation

DOI10.1515/jaa-2021-2058zbMath1491.35142arXiv2104.00133OpenAlexW3197025995MaRDI QIDQ2671530

Maximilian Klumpp, Guido Schneider

Publication date: 3 June 2022

Published in: Journal of Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.00133

zbMATH Keywords

approximationHelmholtz equation

Mathematics Subject Classification ID

Theoretical approximation in context of PDEs (35A35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances
• ASYMPTOTIC DECAY OF A ONE-DIMENSIONAL WAVE PACKET IN A NONLINEAR DISPERSIVE MEDIUM
• The validity of modulation equations for extended systems with cubic nonlinearities
• Nonlinear PDEs
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