A method assuming linear rational Koopman eigenfunctions turns quadratic ODEs into polynomial systems whose algebraic-geometry solutions identify families with closed-form analytical solutions.
Learning Koopman Eigenfunctions and Invariant Subspaces From Data: Symmetric Subspace Decomposition.IEEE Transactions on Automatic Control, 67(7):3442–3457, July 2022
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Analytical solutions for some quadratic ODEs found via linear rational eigenfunctions and the rational eigenfunction variety
A method assuming linear rational Koopman eigenfunctions turns quadratic ODEs into polynomial systems whose algebraic-geometry solutions identify families with closed-form analytical solutions.