The propagation in a rarefied plasma (n(e) < or approximately 10(15) cm(-3)) of collisionless shock waves and ion-acoustic solitons, excited following the interaction of a long (tauL approximately 470 ps) and intense (I approximately 10(15) W cm(-2)) laser pulse with solid targets, has been investigated via proton probing techniques. The shocks' structures and related electric field distributions were reconstructed with high spatial and temporal resolution. The experimental results were interpreted within the framework of the nonlinear wave description based on the Korteweg-de Vries-Burgers equation.