In this paper we consider one-dimensional wave propagation problems, with suitable boundary conditions, reformulated using space-time boundary integral equations with retarded potential. In the first part, special attention is devoted to a formulation based on a natural energy identity that leads to a space-time weak formulation of the corresponding boundary integral equations with robust theoretical properties. Continuity and coerciveness of the bilinear form related to the energetic formulation are proved. Then we compare the new energetic weak formulation with different other time-domain boundary element method procedures applied to wave propagation analysis in layered media. The paper concludes with several numerical tests to demonstrate the effectiveness of the introduced technique in the numerical solution of Dirichlet-Neumann problems in their integral formulation, pointing out the numerical properties of the derived linear systems.
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