Solitary waves and their interactions in the cylindrical Korteweg-de Vries equation

TL;DR

This paper investigates solitary wave solutions of the cylindrical Korteweg-de Vries equation, analyzing their types, parameter dependence on distance, and interactions through approximate, exact, and numerical methods.

Contribution

It provides a comprehensive analysis of solitary waves in the cylindrical KdV equation, including classification, parameter dependence, and interaction dynamics, which were not previously detailed.

Findings

Identification of different solitary wave types

Parameter dependence of waves on distance

Interaction behaviors between different wave types

Abstract

We consider approximate, exact, and numerical solutions to the cylindrical Korteweg-de Vries equation. We show that there are different types of solitary waves and obtain the dependence of their parameters on distance. Then, we study the interaction of solitary waves of different types.