Two Distinct Approaches for Analytical Solutions and Painlevé Integrability of the (3 + 1)-Dimensional Variable Coefficient KP Equation Describing Long Waves in Shallow Water
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Shailendra Singh [1] ; S. Saha Ray [2]
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[1] Siksha O Anusandhan University
Siksha O Anusandhan University
India
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[2] IIEST Shibpur
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
- Idioma: inglés
- Enlaces
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Resumen
This study focuses on the (3+1)-dimensional extended Kadomtsev-Petviashvili (KP) equation with variable-coefficients, which serves as an important model for describing the propagation of long waves in shallow water and plasma environments where physical properties such as depth, density, or magnetic field strength vary dynamically. The Painlevé analysis technique is used to demonstrate the integrability of the equation under consideration. Using this procedure, the integrable version of the given equation is successfully obtained. The auto-Bäcklund transformation (ABT) approach is employed to provide various analytical solutions in the form of complex, rational, exponential, and linear ones. Moreover, the closed-form solitary wave solutions for this equation are obtained by the Paul-Painlevé method (PPM). All of the solutions are shown as three-dimensional plots where the desired outcomes are obtained by varying the parameters and variable coefficients. These graphs show the many sides of the complex periodic wave surfaces and several forms of periodic waves for the concerned problem. The resulting wave solutions can be applied to the analysis of fluid flow wave patterns as well as ocean wave behavior. There are numerous physical applications for the suggested method of simplifying nonlinear dynamical models.
This analysis will likely be of interest to a wide range of scholars, researchers, and professionals in nonlinear physics and engineering models. Overall, this work not only establishes the integrability of the VeKP equation but also provides new families of exact analytical solutions. The combination of Painlevé analysis, ABT, and PPM demonstrates a novel and versatile approach for studying nonlinear wave equations with variable coefficients.
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