  The present work studies deeply quadratic symplectic Lie superalgebras,
obtaining, in particular, that they are all nilpotent. Consequently, we provide
classifications in low dimensions and identify the double extensions that
maintain symplectic structures. By means of both elementary odd double
extensions and generalized double extensions of quadratic symplectic Lie
superalgebras, we obtain an inductive description of quadratic symplectic Lie
superalgebras of filiform type.
