Stroboscopic averaging of highly oscillatory nonlinear wave equations

DOI10.1002/mma.3183zbMath1322.34069OpenAlexW2057246381MaRDI QIDQ5259871

G. Leboucher

Publication date: 29 June 2015

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.3183

zbMATH Keywords

nonlinear wave equationstroboscopic averaginghighly oscillatory evolution equation

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25)

Cites Work

• Energy cascades for NLS on the torus
• Higher-order averaging, formal series and numerical integration. I: B-series
• Numerical stroboscopic averaging for ODEs and DAEs
• Semigroups of linear operators and applications to partial differential equations
• Multiphase averaging for classical systems. With applications to adiabatic theorems. Transl. from the French by H. S. Dumas
• Birkhoff normal form for some nonlinear PDEs
• Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations
• Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions
• A Stroboscopic Numerical Method for Highly Oscillatory Problems
• Modulated Fourier expansions and heterogeneous multiscale methods
• Higher Order Averaging and Related Methods for Perturbed Periodic and Quasi-Periodic Systems
• Averaging methods in nonlinear dynamical systems

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