Any two symplectic forms on a p-adic analytic manifold are locally isomorphic, and second-countable p-adic analytic symplectic manifolds are classified by their p-adic volume.
Darboux: Sur le probl` eme de Pfaff.Bulletin des sciences math´ ematiques et astronomiques 2e s´ erie6(1) (1882), 14–36
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Darboux's Theorem in $p$-adic symplectic geometry
Any two symplectic forms on a p-adic analytic manifold are locally isomorphic, and second-countable p-adic analytic symplectic manifolds are classified by their p-adic volume.