OPTIMAL SYSTEM OF 1-D SUBALGEBRAS AND CONSERVED QUANTITIES OF A NONLINEAR WAVE EQUATION IN THREE DIMENSIONS ARISING IN ENGINEERING PHYSICS

Abstract

The construction of explicit structures of conserved vectors plays diverse crucial roles in the study of nonlinear science inclusive of the fact that they are invoked in developing appropriate numerical schemes and for other mathematical analyses. Therefore, in this paper, we examine the conserved quantities of a nonlinear wave equation, existing in three dimensions, and highlight their applications in physical sciences. The robust technique of the Lie group theory of differential equations (DEs) is invoked to achieve analytic solutions to the equation. This technique is used in a systematic way to generate the Lie point symmetries of the equation under study. Consequently, an optimal system of one-dimensional (1-D) Lie subalgebras related to the equation is obtained. Thereafter, we engage the formal Lagrangian of the nonlinear wave equation in conjunction with various gained subalgebras to construct conservation laws of the equation under study using Ibragimov's theorem for conserved vectors