Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev-Petviashvili equation

In this paper, we take into consideration a general form of the extended Kadomtsev-Petviashvili equation, which has several applications in applied sciences and engineering. The Painleve analysis via WTC-Kruskal algorithm is first used to validate the integrability of this nonlinear model. Thereafter, we determine the multi-solitons, breather solutions, lump waves, rouge waves, lump with solitary waves interaction, and breather with solitons interaction by using various ansatz's functions based on bilinear formalism and symbolic computation. The solitary wave ansatz method is used to extract the bight solitons, dark solitons, singular solitons, and the periodic function solutions. In addition, the Ma-breather, Kuznetsov-Ma breather, and their associated rogue wave solutions are also discussed. In order to demonstrate several physical structures, the figures relating to these solutions are illustrated by selecting appropriate parametric values in 2D, 3D, and contour plots with the assistance of the symbolic package Mathematica 13.1. The dynamics of nonlinear wave models are addressed by these solutions.

Automated summary

This paper focuses on studying various solutions and their applications in nonlinear wave models for the extended Kadomtsev-Petviashvili equation. The integrability of the equation is validated using Painleve analysis and WTC-Kruskal algorithm. Different types of solutions are determined using various ansatz's functions and symbolic computation. Visualization of the solutions is performed by selecting appropriate parametric values and utilizing Mathematica 13.1.