The solitonic, periodic and quasiperiodic solutions that obey the full system of transport equations describing one-dimensional motion of a isotropic collisionless quasineutral plasma in a magnetic field are treated. The domains of physical parameters of such a plasma are determined for fast and slow magnetoacoustic branches, where solitary waves and generalized solitary waves exist. In the parameter domain where solitary waves are replaced by non-local generalized solitary waves, the localized disturbances are subject to decay, which has qualitatively different mechanisms for fast and slow magnetoacoustic waves. The specific feature of the decay process for fast waves is found to be characterized by a decrease of energy of the disturbance due to quasistationary radiation of a resonant periodic wave of the same nature. Analogous disturbances, having the form of a slow magnetoacoustic solitary wave core, practically do not radiate resonant Alfvénic modes, but rapidly lose energy as a result of continuous shedding of a slow-wave component. Various types of shock waves are also considered. Their structure is formed by existing solitonic configurations – solitary and generalized solitary waves. Possibilities of observations of solitary waves and their decay in a real plasma are discussed.