On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation
نویسندگان
1 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.
2 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.
3 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.
doi
10.22034/cmde.2024.60476.2589چکیده
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.
