A rigorous justification of the Matthews-Cox approximation for the Nikolaevskiy equation

DOI10.1016/j.jde.2017.02.005zbMath1364.35074OpenAlexW2587122875MaRDI QIDQ515504

Yong-Cai Geng, Sumit K. Garg

Publication date: 16 March 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2017.02.005

zbMATH Keywords

multiscale analysisamplitude equationsmodulation equationsGinzburg-Landau scaling ansatz

Mathematics Subject Classification ID

Initial value problems for nonlinear higher-order PDEs (35G25) Pattern formations in context of PDEs (35B36)

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Rotating Shallow Water Equations with Bottom Drag: Bifurcations and Growth Due to Kinetic Energy Backscatter

Cites Work

• The NLS approximation makes wrong predictions for the water wave problem in case of small surface tension and spatially periodic boundary conditions
• Geometric theory of semilinear parabolic equations
• A model for nonlinear seismic waves in a medium with instability
• Error estimates for the Ginzburg-Landau approximation
• Justification of the Ginzburg-Landau approximation in case of marginally stable long waves
• Justification and failure of the nonlinear Schrödinger equation in case of non-trivial quadratic resonances
• Validity and Limitation of the Newell‐Whitehead Equation
• Justification of the Ginzburg–Landau approximation for an instability as it appears for Marangoni convection

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