https://doi.org/10.1140/epjp/s13360-025-06222-2
Regular Article
Study of (3+1)-Dimensional Kadomtsev–Petviashvili Equation with Source Term through Painlevé Integrability and Lie Symmetry Analysis
Department of Mathematics, Visvesvaraya National Institute of Technology, 440010, Nagpur, Maharashtra, India
Received:
25
November
2024
Accepted:
16
March
2025
Published online:
11
April
2025
In this article, we consider the generalized (3+1)–dimensional Kadomtsev–Petviashvili equation with source term. At the outset, it is revealed that this equation does not possess Painlevé integrability. Thereafter, employing a transformation of the dependent variable, an exact solution is derived. Following this, we use the classical Lie symmetry analysis, and through the art of similarity reduction several exact solutions are procured, including those of periodic nature. Further, by means of a traveling wave transformation, a variety of solutions are brought forth, such as rational, exponential, periodic, kink-type, and anti-kink-type solitons, these being achieved through the method of differential constraints. Finally, solutions are exhibited graphically for clearer comprehension.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
