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

Abstract

<abstract><p>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^\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.</p></abstract>