Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations

TL;DR

This paper reviews mathematical results on KP equations and uses numerical simulations to analyze blow-up, stability, and long-term behavior of solutions, focusing on solitary waves.

Contribution

It provides a numerical investigation into the blow-up and stability properties of solutions to generalized KP equations, complementing existing mathematical results.

Findings

Identification of conditions leading to blow-up or stability

Numerical evidence of long-time behavior of solutions

Insights into solitary wave stability and instability

Abstract

We first review the known mathematical results concerning the KP type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations : blow-up versus long time behavior, stability and instability of solitary waves.