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The tachyon field of p-adic string theory is made noncommutative by replacingordinary products with noncommutative products in its exact effective action.The same is done for the boundary string field theory, treated as the p -> 1limit of the p-adic string. Solitonic lumps corresponding to D-branes areobtained for all values of the noncommutative parameter theta. This is incontrast to usual scalar field theories in which the noncommutative solitons donot persist below a critical value of theta. As theta varies from zero toinfinity, the solution interpolates smoothly between the soliton of the p-adictheory (respectively BSFT) to the noncommutative soliton.Comment: 1+14 pages (harvmac b), 1 eps figure, v2: references added, typos  correcte

Exact noncommutative solitons in p-adic strings and BSFT