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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Dynamics of Exact Solutions and Conserved Quantities of 2D Generalized Ablowitz-Kaup- Newell-Segur Water Wave Equation in Fluid Mechanics using Symmetry Group Technique

Journal of Vibration Testing and System Dynamics 10(1) (2026) 53--81 | DOI:10.5890/JVTSD.2026.03.004

Oke Davies Adeyemo, Chaudry Masood Khalique

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

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Abstract

This article examines analytically, a fourth-order nonlinear generalized Ablowitz-Kaup-Newell-Segur water wave equation in fluid dynamics with a perturbation parameter. Utilizing the Lie theoretic approach, symmetries of the equation are secured and used to gain invariant solutions. We achieve various analytic solutions of the understudy equation through the techniques of Lie symmetry reductions together with direct integration which include elliptic, trigonometry and algebraic functions. We obtain periodic functions solutions of the equation. The power series solution of the equation is generated. Moreover, the Kudryashov technique is utilized whereby gaining hyperbolic function solution of the equation. We present graphical depictions of the results for more meaningful interpretation and discuss them. Conclusively, we secure conserved quantities of the aforementioned equation by employing both the general multiplier and Noether techniques. Moreover, the applications of various results achieved in the study in physical sciences are outlined which saw to the physical interpretations of the conserved vectors being explicated.

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