You have butted spokes. They're thicker at both ends for added strength at the critical points where breakage occurs. You're best off replacing them with similar spokes which are readily available, though more costly.
Most better shops will be able to give you an almost exact replacement for your spokes, though the length of the thicker section varies from brand to brand. If not at the shop, you can buy them online.
Note, replace the nipples at the same time.
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