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We explore perturbations to a kink-like (codimension 1) topological defectwhose world brane is $AdS_{q}$ embedded into $AdS_{q+1}$. Previously, we foundsolutions in the limit the mass of the scalar field vanishes. In this articlewe extend a calculation previously done in $AdS_{2}$ to higher-dimensionalembedding spaces and find that all perturbations to the mass of the field arestable to first order as expected in a theory with topological defects. We findthat the equation of motion to the correction strongly resembles a problemwell-known in quantum mechanics.

Perturbations to Generalized Kink-like Topological Defects in $AdS$