# Exploring soliton solutions and dynamical features of three dimensional Gardner Kadomtsov Petviashvili equation

## TL;DR

This paper explores the behavior of waves in a three-dimensional equation using mathematical methods to reveal patterns and dynamics.

## Contribution

The paper introduces new wave solutions and analyzes chaotic behavior in the three-dimensional Gardner-Kadomtsov-Petviashvili equation.

## Key findings

- Wave solutions show distinct behaviors based on parameter changes.
- Numerical simulations reveal periodic and super nonlinear wave patterns.
- Chaotic behavior is identified through Lyapunov exponents and Poincaré maps.

## Abstract

In this paper, the dynamical features and soliton structures of the Gardner-Kadomtsov-Petviashvili equation in three dimensions are looked at. The Jacobi elliptic function method yields wave solutions that display distinct behaviors based on parameter variations. We reformulate the system into a planar dynamical system via the Galilean transformation for further analysis.Phase portraits are depicted by adjusting the bifurcation parameters , while periodic and super nonlinear periodic wave solutions are portrayed using numerical simulations. Furthermore, quasi-periodic and chaotic behavior is depicted by varying the external forcing term and using tools such as Lyapunov exponents, Poincaré maps, and sensitivity analysis. Changes in frequency and amplitude strongly influence the system’s dynamics, offering insights that can improve predictions, enhance control methods, and optimize model performance.