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              <p>This paper is devoted to the construction of periodic solutions of non-linear Schrödinger equations on the torus, for a large set of frequencies. Usual proofs of such results rely on the use of Nash-Moser methods. Our approach avoids this, exploiting the possibility of reducing, through para-differential conjugation, the equation under study to an equivalent form for which periodic solutions may be constructed by a classical iteration scheme.</p>
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