An optimal System of Lie Subalgebras and Group-Invariant Solutions with Conserved Currents of a (3+1)-D Fifth-Order Nonlinear Model I with Applications in Electrical Electronics, Chemical Engineering and Pharmacy

Higher-dimensional nonlinear integrable partial differential equations are significant as they often describe diverse phenomena in nonlinear systems like laser radiations in a plasma, optical pulses in the glass fibres, fluid mechanics, radio waves in the ion sphere, condensed matter and electromagnetics. This article shows an analytical investigation of a (3+1)-dimensional fifth-order nonlinear model with KdV forming its main part. Lie group analysis of the model is performed through which its infinitesimal generators are obtained. These generators are engaged in the construction of an optimal system of Lie subalgebra in one dimension. Moreover, members of the system secured are utilized in reducing the underlying model to ordinary differential equations (ODEs) for possible exact solutions. In consequence, we achieve various functions, ranging from trigonometric, logarithmic, rational, to hyperbolic. In addition, the results found constitute diverse solitonic solutions such as complex, topological kink and anti-kink, trigonometric and bright. We utilize the power series technique to obtain a series solution of the most complicated ordinary differential equation with forty-four terms. In addition, we reveal the dynamics of these solutions via graphical depictions. In the end, we constructed conserved currents of the underlying equation through the use of the multiplier technique. Further, we utilize the optimal system of the underlying model to derive more conserved vectors using Ibragimov's theorem for conservation laws.