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

  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},
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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