Exploring the (3+1)-generalized Kadomtsev-Petviashvili equation: symmetries, reductions, and exact solutions
Year: 2025
Type: article
Abstract: This study establishes a unified approach to utilising symmetry methods to uncover diverse analytical solutions and provides deeper insights into the nonlinear phenomena governed by the Kadomtsev Petviashvili (KP) framework. The (3+1) dimensional generalized Kadomtsev-Petviashvili (gKP) equation with arbitrary nonlinearity f(u) is examined for its underlying symmetry properties, optimal systems, and exact solutions. We employ Lie symmetry methods to classify the algebraic structure and develop one-dimensional optimal systems for different nonlinearities, including power and exponential forms of f(u). Additionally, using square-law nonlinearity, we derive the modified Korteweg–de Vries-Kadomtsev Petviashvili (mKdV-KP) equation, which is then subjected to symmetry analysis. By utilising the invariants, we systematically reduce the (3+1) gKP equation to lower-dimensional forms, facilitating the discovery of static and travelling wave solutions. Notably, the square-law nonlinearity reveals rich solution behaviour, which includes elliptic and Jacobi function representations. Furthermore, graphical illustrations provide a better understanding of underscoring their relevance to soliton theory and nonlinear wave dynamics.
Source: Physica Scripta
Authors: J Mohammed Zubair Ahamed, R Sinuvasan
Institution: VIT-AP University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,400
OpenAlex ID: W4408902005