Invariance analysis for determining the classical solutions, optimal system, and conserved vectors of generalized higher-dimensional Ablowitz-Kaup- Newell-Segur equation in theoretical physics

In the world of evolution equations, higher dimensional nonlinear partial differential equation has attracted a vast attention for investigation due to the fact that, it models various interesting physical phenomena existent in, fluids dynamics (theoretical physics), other nonlinear sciences and engineering. In the wake of this, analytical examination of a nonlinear generalized Ablowitz-Kaup-Newell-Segur water wave equation arising from theoretical physics is the given consideration in this article. Leveraging on the robust Lie group theoretic approach, applied to differential equations, one investigates the understudy equation in a detailed form with a view to securing various results of interest. Thus, in executing these, one first computes a seven-dimensional Lie algebra L7 associated to the nonlinear generalized Ablowitz-Kaup-Newell-Segur water wave equation in a stepwise structure. Sequel to this, one parameter groups of transformation associated to L7, is studied. Additionally, commutation relations and adjoint representations of the Lie algebra are tabularly explicated. A detailed computation of a one dimensional optimal system associated to L7 is furnished. Thereafter, various obtained sub-algebras are invoked in effectuating reductions of the model under examination to ordinary differential equations, so that diverse pertinent exact solutions are attained. The success in this regard entrenched solutions like trigonometric, exponential, logarithmic and hyperbolic functions. Besides, algebraic solutions among which arbitrary functions exist and quadrature are found. Sound knowledge of these results are further engendered by numerically simulating them. Wave structures of diverse interests are achieved. Furthermore, conservation laws of the equation are calculated via conserved vectors theorem by Ibragimov using the related formal Lagrangian to the model.