Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition
Pattern Formation and Solitons
2026-04-27 v1
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.
Cite
@article{arxiv.2604.22389,
title = {Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition},
author = {Alexey Samokhin},
journal= {arXiv preprint arXiv:2604.22389},
year = {2026}
}
Comments
12 pages, 5 figures