The author considers non-linear waves propagating at an angle to the external magnetic field in a multi-component, completely ionized, quasi-neutral plasma. Collisions between plasma particles are not taken into account. For waves propagating across the magnetic field, thermal effects are taken into account by means of Vlasov kinetic equations. The author finds dispersion effects due to deviation of the dispersion law ω = ω(k) from a linear one. An analytical expression is obtained for the profile of an isolated wave of low amplitude and it is found that, depending on the angle between the magnetic field and the velocity of wave propagation, the wave can be a non-linear compression or rarefaction wave. The necessary conditions limiting changes in the Mach number are established. The fine structure of the solitary wave is investigated for a three-component plasma, allowance being made for effects associated with electron inertia. It is found that the depression i n the solitary compression wave appears only when the ions of both sorts are positively charged. The critical Mach number (M*) and magnetic field strength (h*) values are obtained. For M > M* there is a depression in the solitary compression wave.