Salt tectonics is placed within the theory of nonlinear dynamical systems. Features such as waves, diapirs, and tears are viewed as natural consequences of the symmetry breaking instabilities and related self-organized dynamics of the deforming salt body coupled to the reaction, transport, and mechanics of the surrounding sediments. The fundamental nonlinearities are in the surrounding-rock and salt rheology. Our findings are based on a coupled RTM model simulated using finite element techniques. The centerpiece of the rheology of both rocks and salt is a nonlinear incremental stress formulation that integrates poroelasticity, continuous irreversible mechanical deformation (with yield behavior), pressure solution, and fracturing. In contrast to previously presented studies, in our approach the descriptive variables of all solid and fluid phases (stress, velocity, concentrations, etc.) and porous media (texture, i.e., volume fractions, composition, etc.) are solved from RTM equations accounting for interactions and interdependencies between them. The role of the coupling between the spatial distribution of sediment input rate and diapir growth and stalling is examined as is the creation of an array of salt tectonic minibasins.