Conditional invariance of the nonlinear wave equation (Q1174884)

The authors consider the equation \(u_{tt}-\nabla[f(u)\nabla u]=F(x,u,Du)\) where \(f(u)>0\), \(Du=(u_ t,u_ 1,\dots,u_ n)\), \(u_ \mu=\partial u/\partial x_ \mu\). By using Lie's method, conditional invariance of the above equation and Lie invariance of the equation \[ u_ t^ 2-f(u)(\nabla u)^ 2=m,\qquad m=const \] are investigated. The notion ''conditional invariance'' was considered in previous works of the authors.