On the propagation of weak nonlinear waves in the alluvial inclined channel when x >> 1

The propagation of weak nonlinear waves in the alluvial inclined channel when x >> 1 (here X = H0/ L0 sin α, H0 is the average depth, L0 is the characteristic length along the flow, α is the inclined angle between the undisturbed bottom and the horizontal direction) is investigated by the multistate method. It shows that arbitrary localized perturbations will be split into three modes. The nonlinear differential equations describing the evolution of those modes are delivered. Their solutions are thus analyzed.