Physica D 142 ( 2000 ) , 1-19 Reconstruction Equations and the Karhunen-Loève Expansion for Systems with Symmetry

@inproceedings{Rowley2000PhysicaD1,
  title={Physica D 142 ( 2000 ) , 1-19 Reconstruction Equations and the Karhunen-Lo{\`e}ve Expansion for Systems with Symmetry},
  author={Clarence W. Rowley and Jerrold E. Marsden},
  year={2000}
}
We present a method for applying the Karhunen-Loève decomposition to systems with continuous symmetry. The techniques in this paper contribute to the general procedure of removing variables associated with the symmetry of a problem, which has been used in previous works both to identify coherent structures in solutions of PDEs, and to derive low-order models via Galerkin projection. The main result of this paper is to derive a simple and easily implementable set of reconstruction equations… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 21 references

Reconstructing phase space from PDE simulations

  • M. Kirby, D. Armbruster
  • Z. Angew. Math. Phys.,
  • 1992
Highly Influential
11 Excerpts

Introduction to Mechanics and Symmetry

  • J. E. Marsden, T. S. Ratiu
  • Texts in Applied Mathematics,
  • 1994
Highly Influential
3 Excerpts

Order and complexity in the Kuramoto-Sivashinski model of weakly turbulent interfaces

  • J. M. Hyman, B. Nicolaenko, S. Zaleski
  • Phys. D,
  • 1986
Highly Influential
4 Excerpts

Robust system analysis and nonlinear system model reduction

  • S. Glavaški
  • Ph. D. Thesis, California Institute of Technology…
  • 1998
Highly Influential
9 Excerpts

Galerkin projections and the proper orthogonal decomposition for equivariant equations

  • G. Berkooz, E. S. Titi
  • Phys. Lett. A,
  • 1993
Highly Influential
6 Excerpts

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