Abstract We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the N $$ \mathcal{N} $$ = 1 supersymmetry. This is related to the fact that in the bosonic sector (i. e. https://countryscenesaddleryandpetsuppliers.shop/product-category/western-bridles-2/