Mathematical Methods in Wave Propagation: Part II‐‐Non‐Linear Wave Front Analysis

Summary

This work continues the account given in Part I of the paper¹ by presenting a short summary of some of the mathematical techniques employed in the wave front analysis of quasi‐linear hyperbolic partial differential equations. Starting from a number of important physical examples, the classification of quasi‐linear first‐order systems is discussed and followed by a simple account of the theory of characteristics for systems involving n dependent and two independent variables. A special example is discussed showing how discontinuities arise in solutions, and the paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics.