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 existing in three dimensions. The Lie symmetry analysis of the equation is carried out step-by-step. In consequence, we found symmetries from which various group-invariant solutions results from which numerous solutions of interest that satisfy the KP-BBM equation are obtained. Solutions of interest secured include hyperbolic functions as well as elliptic functions with the latter being the more general of the two solutions. Besides, a good number of algebraic solutions with arbitrary functions are also achieved. Moreover, the dynamics of the solutions are further explored diagrammatically using computer software. In the concluding part, various conservation laws of the underlying model are constructed via the multiplier method as well as the Noether theorem.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 06 May 2024

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History

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

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