In this paper we show the existence of one-dimensional solitons (travelling waves of finite energy) for a generalized nonlinear dispersive equation modeling the deformations of a hyperelastic compressible plate. From the Hamiltonian structure for such equation we find the natural space for the travelling wave solutions and characterize travelling waves variationally as minimizers of an energy functional under a suitable constraint. Our approach involves the Lions's Concentration-Compactness Lemma.