Lie analysis, conserved vectors, nonlinear self-adjoint classification and exact solutions of generalized $\left(N+1\right)$-dimensional nonlinear Boussinesq equation

In this article, the generalized $\left(N+1\right)$-dimensional nonlinear Boussinesq equation is analyzed via Lie symmetry method. Lie point symmetries of the considered equation and accompanying invariant groups are computed. After transforming the equation into a nonlinear ordinary differential equation (ODE), analytical solutions of various types are obtained using the $\left(G^{\mathrm{\prime }}/G,1/G\right)$ expansion method. The concept of nonlinear self-adjointness is used in order to determine nonlocal conservation laws of the equation in lower dimensions. By selecting the appropriate parameter values, the study provides a graph of the solutions to the equation under study.