Group analysis of the one dimensional wave equation with delay

Abstract

In this paper, we establish a Lie type invariance condition for second order delay partialdifferential equations. The determining equations are obtained using Taylor’s theorem fora function of several variables. The symmetries of the wave equation with delay, its kerneland extensions of the kernel have been found. We make a complete group classification ofthe wave equation containing an arbitrary differentiable functional with delay, for whichthere is no existing literature. Further, the complete set of invariant solutions led by thisclassification have been found.