Lines or surfaces associated with a partial differential equation, or with a set of such equations, which are at all points tangent to characteristic directions, determined by certain specified linear combinations of the equations. The use of these lines or surfaces may facilitate the solution of the equations and is known as the method of characteristics. The method has been particularly successful, for example, in the problem of finite-amplitude expansion and shock waves, and the analogy between certain of these flows and a traveling disturbance on an inversion has been studied by meteorologists.