Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation (Q886166)

This paper is devoted to nonlocal symmetries of the nonlinear wave equation \(u_{tt}=(c^2(u)u_x)_x\). A tree of nonlocally related potential systems and subsystems for this equation is constructed. In particular, it is shown that for every nonlinear wave equation there exists a nonlocal transformation that relates this equation to a linear wave equation \(u_{tt}=d^2(x)u_{xx}\) such that to every solution of the initial equation there is a corresponding solution of the linear one and vice versa. Nonlocal symmetries that are point symmetries of other equations of the tree are calculated.