ABSTRACT
This chapter discusses the sequel travelling or simple waves for hyperbolic and diffusive systems. It describes the simple wave solutions in the context of one-dimensional gasdynamics and explores the later to systems of both homogeneous and inhomogeneous hyperbolic systems. The discussion of ODEs governing permanent waves is supplemented by J. H. Merkin and M. A. Sadiq by the numerical solutions of IVP for original partial differential equations (PDE) to determine which kind of travelling waves finally emerge as large-time asymptotics. The systems of nonlinear PDEs describing physical problems, particularly in geophysics, have some inhomogeneous term(s) on the right-hand sides arising from external forces such as gravity and frictional effects. The original system of nonlinear PDEs is a coupled eighth-order one; thus, the exact reduction to a single second-order ODE is rather unusual. The chapter considers the motion of a two-dimensional compressible, nonviscous, and perfectly electrically-conducting fluid which is stratified in the vertical direction.
