On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation

Document Type : Research Paper

Authors

Material Science, Innovation and Modelling Research Focus Area, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, Republic of South Africa.

Abstract

This paper examines a high-dimensional non-linear partial differential equation called the generalized Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation exists in three dimensions. The Lie symmetry analysis of the equation is carried out step-by-step. As a result, we found symmetries from which various group-invariant solutions arise, leading to numerous solutions of interest that satisfy the KP-BBM equation. Secured solutions of interest include hyperbolic functions and elliptic functions, with the latter being the more general of the two solutions. Additionally, a significant number of algebraic solutions with arbitrary functions are also obtained. Furthermore, the dynamics of the solutions are further explored diagrammatically using computer software. In the concluding section, various conservation laws of the underlying model are derived via the multiplier method and the Noether theorem. 

Keywords

Main Subjects

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Computational Methods for Differential Equations
Volume 13, Issue 2
March 2025
Pages 682-708

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History

  • Receive Date: 08 February 2024
  • Revise Date: 03 April 2024
  • Accept Date: 13 April 2024

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