This paper presents a method for solving classical equations for scalars and gravity in five dimensions, applied to recent suggestions for brane-world phenomenology. The method involves first-order differential equations and is inspired by gauged supergravity but does not require supersymmetry. The authors first apply this method to a nonlinear treatment of a stabilization mechanism for inter-brane spacing. They show that the spacing is uniquely determined after conventional fine-tuning to achieve zero four-dimensional cosmological constant. If the fine-tuning is imperfect, the four-dimensional branes can be de Sitter or anti-de Sitter spacetimes. The authors then construct smooth domain wall solutions that approach any desired array of sharply localized positive-tension branes. They also suggest a construction of a supergravity c-function for non-supersymmetric four-dimensional renormalization group flows. The equations for fluctuations about an arbitrary scalar-gravity background are studied. It is shown that all models with an effectively compactified fifth dimension contain a massless graviton. The graviton is the constant mode in the fifth dimension. The separated wave equation can be recast into the form of supersymmetric quantum mechanics. The graviton wave-function is then the supersymmetric ground state, and there are no tachyons. The paper discusses the five-dimensional gravitational action and the metric with four-dimensional Poincaré symmetry. It presents the Goldberger-Wise mechanism for stabilizing the size of an extra dimension in the brane-world scenario. The authors show that the length of the interval $ S^{1}/Z_{2} $ can be stabilized without fine-tuning the parameters of the model. They also discuss the equations for linear fluctuations about a gravity-scalar-brane configuration and show that the graviton is the supersymmetric ground state, with no tachyons. The paper presents an explicit model with a quadratic $ W(\phi) $, $ \lambda_{1}(\phi) $, and $ \lambda_{2}(\phi) $ that are tangent to one another. The authors show that the brane spacing is determined by the condition $ br_{0} = \ln(\phi_{1}/\phi_{2}) $. They also discuss the implications of the model for the gauge hierarchy problem and the robustness of the mechanism for generating large numbers. The paper concludes with a discussion of the numerical results for the model, showing the behavior of the solutions in the t-x plane.This paper presents a method for solving classical equations for scalars and gravity in five dimensions, applied to recent suggestions for brane-world phenomenology. The method involves first-order differential equations and is inspired by gauged supergravity but does not require supersymmetry. The authors first apply this method to a nonlinear treatment of a stabilization mechanism for inter-brane spacing. They show that the spacing is uniquely determined after conventional fine-tuning to achieve zero four-dimensional cosmological constant. If the fine-tuning is imperfect, the four-dimensional branes can be de Sitter or anti-de Sitter spacetimes. The authors then construct smooth domain wall solutions that approach any desired array of sharply localized positive-tension branes. They also suggest a construction of a supergravity c-function for non-supersymmetric four-dimensional renormalization group flows. The equations for fluctuations about an arbitrary scalar-gravity background are studied. It is shown that all models with an effectively compactified fifth dimension contain a massless graviton. The graviton is the constant mode in the fifth dimension. The separated wave equation can be recast into the form of supersymmetric quantum mechanics. The graviton wave-function is then the supersymmetric ground state, and there are no tachyons. The paper discusses the five-dimensional gravitational action and the metric with four-dimensional Poincaré symmetry. It presents the Goldberger-Wise mechanism for stabilizing the size of an extra dimension in the brane-world scenario. The authors show that the length of the interval $ S^{1}/Z_{2} $ can be stabilized without fine-tuning the parameters of the model. They also discuss the equations for linear fluctuations about a gravity-scalar-brane configuration and show that the graviton is the supersymmetric ground state, with no tachyons. The paper presents an explicit model with a quadratic $ W(\phi) $, $ \lambda_{1}(\phi) $, and $ \lambda_{2}(\phi) $ that are tangent to one another. The authors show that the brane spacing is determined by the condition $ br_{0} = \ln(\phi_{1}/\phi_{2}) $. They also discuss the implications of the model for the gauge hierarchy problem and the robustness of the mechanism for generating large numbers. The paper concludes with a discussion of the numerical results for the model, showing the behavior of the solutions in the t-x plane.