A method assuming linear rational Koopman eigenfunctions turns quadratic ODEs into polynomial systems whose algebraic-geometry solutions identify families with closed-form analytical solutions.
Applied Koopmanism.Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4):047510, December 2012
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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.