It is typical in smectic liquid crystals to describe elastic deformations with a linear theory when the elastic strain is small. We extend the recent, exact solution of Brener and Marchenko to more general one-dimensional deformations, including multiple edge dislocations by relying on the Bogomol'nyi, Prasad and Sommerfeld (BPS) decomposition. We introduce an approximation for the deformation profile far from a spherical inclusion and find an enhanced attractive interaction at long distances due to the nonlinear elasticity.