ABSTRACT
We shall discuss in this section a class of solutions, known as simple waves, which are the only known exact solutions (except for some solutions of particular equations) and which can be easily evaluated numerically. These are plane or one-dimensional wave solutions of what is known as a reducible system of equations, in which the coefficient matrices A and B’s (either in (2.1.1) or (2.3.7)) are functions of u only and the nonhomogeneous term is absent i.e., C = 0. Simple waves form the building block of more general solutions. For example, for a reducible pair of equations, any solution in a characteristic quadrilateral type of domain bounded by two pairs of intersecting characteristic curves of different families can not only be obtained as a result of interaction of a pair of simple waves but can also give rise to such a pair. We shall also see later in this chapter that a large class of solutions which are obtained in high frequency limit are extensions or modifications of simple wave solutions. We start with an example of a simple wave.
