Multi-bifurcations of Wavefronts on r-corners

TL;DR

This paper extends reticular Legendrian unfoldings to analyze multi-time bifurcations of wavefronts on r-corners, providing a classification of generic bifurcations with visual representations.

Contribution

It introduces a new framework for studying multi-time bifurcations of wavefronts on r-corners and classifies generic stable bifurcations with detailed figures.

Findings

Classification list of generic bifurcations with two time parameters

All generic figures in the plane and space are provided

Extended the notion of reticular Legendrian unfoldings

Abstract

We extend the notion of reticular Legendrian unfoldings in order to investigate multi-time bifurcations of wavefronts generated by an r-corner. We give a classification list of generic and stable bifurcations with two time parameter and give all generic figures in the plane and the space.