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We study non-linear differential equations on the punctured formal disc byconsidering the natural derived enhancements of their spaces of solutions. Inparticular, by appealing to results of the inverse theory in the calculus ofvariations, we show that a variational formulation of a differential equationis \emph{equivalent} to the residue pairing inducing a (-1)-symplectic form onthe derived space of solutions equipped with a certain decoration of itstangent complex.

Derived Geometry and Non-Linear Differential Equations on the Punctured Disc