Justification of the 2D NLS equation for a fourth order nonlinear wave equation – quadratic resonances do not matter much in case of analytic initial conditions

Author:

Düll Wolf-Patrick,Hermann Alina,Schneider Guido,Zimmermann Dominik

Funder

Deutsche Forschungsgemeinschaft

Publisher

Elsevier BV

Subject

Applied Mathematics,Analysis

Reference19 articles.

1. Solitons and the Inverse Scattering Transform;Ablowitz,1981

2. Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity;Chong;ZAMM Z. Angew. Math. Mech.,2013

3. Photonic Crystals. Mathematical Analysis and Numerical Approximation;Dörfler,2011

4. Justification of the nonlinear Schrödinger equation for a resonant Boussinesq model;Düll;Indiana Univ. Math. J.,2006

5. Justification of the nonlinear Schrödinger equation for the evolution of gravity driven 2d surface water waves in a canal of finite depth;Düll;Arch. Ration. Mech. Anal.,2015

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1. A robust way to justify the derivative NLS approximation;Zeitschrift für angewandte Mathematik und Physik;2023-10-14

2. Validity of the Nonlinear Schrödinger Approximation for the Two-Dimensional Water Wave Problem With and Without Surface Tension in the Arc Length Formulation;Archive for Rational Mechanics and Analysis;2020-10-14

3. Failure of the N ‐wave interaction approximation without imposing periodic boundary conditions;ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik;2020-04-07

4. Justification of the Nonlinear Schrödinger Approximation for a Quasilinear Klein–Gordon Equation;Communications in Mathematical Physics;2017-07-27

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