Abstract
Based on the similarity of the coupled nonlinear Schr\"odinger equations with and without external potentials, a relation is established between their solutions. The external potentials are assumed to modify both amplitudes and phases together with the spatial and temporal variables appearing in the transformation relation. With examples of trap potentials depending linearly and quadratically on the spatial coordinate it is demonstrated how the transformation ansatz works in practice for obtaining atomic solitons of Bose-Einstein condensates consisting of sodium and rubidium atoms when one starts from the known optical soliton solution of the nonlinear Schr\"odinger equation without potential.
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