Reconstructing phase space from PDE simulations

DOI10.1007/BF00916425zbMath0764.35008MaRDI QIDQ1202580

S. Singh

Publication date: 14 February 1993

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

dynamical systems theorychaotic burstingblow up solutionscomplex spatio-temporal structureshomoclinic burstsKarhunen-Loève decomposition (K-L)Kuramoto- Sivashinky equationoptimal Galerkin systempropagation of large scale structures in weak turbulent flame frontsspatially localized oscillationsstrange fixed pointstructure of traveling wave solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Theoretical approximation in context of PDEs (35A35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Bifurcations in context of PDEs (35B32) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09)

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Cites Work

• Unnamed Item
• Low-dimensional dynamics for the complex Ginzburg-Landau equation
• An eigenfunction analysis of axisymmetric jet flow
• Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
• Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
• Spatiotemporal analysis of complex signals: Theory and applications
• Optimal low-dimensional dynamical approximations
• Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
• The dynamics of coherent structures in the wall region of a turbulent boundary layer
• Characteristic-eddy decomposition of turbulence in a channel
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold