Modified energy functionals and the NLS approximation

DOI10.3934/dcds.2017054zbMath1375.35406arXiv1606.00028OpenAlexW2964105928MaRDI QIDQ525517

Patrick Cummings, C. Eugene Wayne

Publication date: 5 May 2017

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.00028

zbMATH Keywords

nonlinear Schrödinger equationmodulation equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Second-order quasilinear hyperbolic equations (35L72)

Related Items

A robust way to justify the derivative NLS approximation ⋮ On the approximation of vorticity fronts by the Burgers–Hilbert equation ⋮ Validity of the nonlinear Schrödinger approximation for quasilinear dispersive systems with more than one derivative ⋮ Validity of the nonlinear Schrödinger approximation for the two-dimensional water wave problem with and without surface tension in the arc length formulation ⋮ Modulation approximation for the quantum Euler-Poisson equation

Cites Work

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• Normal forms and quadratic nonlinear Klein-Gordon equations
• Nonlinear modulation of gravity waves: a rigorous approach
• The validity of modulation equations for extended systems with cubic nonlinearities
• Long time solutions for a Burgers-Hilbert equation via a modified energy method
• Global solutions for the gravity water waves equation in dimension 3

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