# Periodic parabola solitons for the nonautonomous KP equation

## TL;DR

This paper derives and analyzes periodic parabola soliton solutions for the nonautonomous KP equation using Painleve analysis and Hirota bilinear method, revealing parameter constraints and convergence conditions.

## Contribution

It introduces a novel class of solutions for the nonautonomous KP equation with detailed parameter constraints and convergence analysis.

## Key findings

- Six undetermined parameters in the solutions.
- Conditions for the convergence of solutions.
- Features of typical solution cases.

## Abstract

Kadomtsev-Petviashvili (KP) equation, who can describe different models in fluids and plasmas, has drawn investigation for its solitonic solutions with various methods. In this paper, we focus on the periodic parabola solitons for the (2+1) dimensional nonautonomous KP equations where the necessary constraints of the parameters are figured out. With Painleve analysis and Hirota bilinear method, we find that the solution has six undetermined parameters as well as analyze the features of some typical cases of the solutions. Based on the constructed solutions, the conditions of their convergence are also discussed.