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Three types of thick branes, i.e., Poincar\'e, de Sitter, and anti--de Sitter branes, are considered. They are realized as the nonsingular solutions of the Einstein equations with nontrivial dilaton and potentials. The scalar perturbations of these systems are also investigated. We find that the effective potentials of the master equations of the scalar perturbations are positive definite and consequently these systems are stable under small perturbations.
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Kobayashi et al. (2002) studied this question.
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