Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition

Abstract

Spherical and cylindrical KdV-B equations have few known exact solutions, yet these solutions are hard to be interpreted physically. But these equations do have a family of diverging shock waves. Their properties such as asymptotic modes, stability, rules of their interactions/superposition are the subject of this paper. It gives a detailed asymptotic description of the one-parameter families of shock wave solutions and proves their stability using a conservation law. Based on these results, effective rules of superposition are obtained. Moreover these rules are applicable to a wide class of shock waves, in particular discontinuous. Typical examples are illustrated by graphs.