Waves in fluid and solid media

Abstract

‘‘Waves in Fluid and Solid Media’’ is the title of the last unpublished lecture notes of David G. Crighton. The lectures were given at the University of Cambridge and have the date Lent 1998. In these notes Crighton introduces basic notions connected with wave motion, analyzing in particular propagation of sound waves in a compressible fluid as well as dilatational and shear waves in an elastic solid. A part of these lectures is devoted to nonlinear acoustics including the discussion of wave steepening, formation of shocks, Rankine–Hugoniot conditions, Hugoniot adiabatic etc. In my talk the above mentioned ideas will be extended and recent developments in the theory of propagation and interaction of weakly nonlinear waves both in fluid and solid media will be presented [W. Domański, Contemp. Math. 255, 45–61 (2000)].