Geometrical features of a nonlinear wavefront

Abstract

We use the equations of weakly nonlinear ray theory (WNLRT), developed by us over a number of years, to study all possible shapes which a nonlinear wavefront in a polytropic gas can have. As seen in experiments, a converging nonlinear wavefront avoids folding itself in a caustic region of a linear theory and emerges unfolded with a pair of kinks. We review the work of Baskar, Potadar and Szeftel showing the way in which the solution of a Riemann problem of the conservation form of the equations of WNLRT can be used to study the formation of new shapes of a nonlinear wavefront from a single singularity on it. We also study the ultimate result of interactions of elementary shapes on the front.