Uniqueness of conservative solutions for nonlinear wave equations via characteristics

For some classes of one-dimensional nonlinear wave equations, solutions are Holder continuous and the ODEs for characteristics admit multiple solutions. Introducing an additional conservation equation and a suitable set of transformed variables, one obtains a new ODE whose right hand side is either Lipschitz continuous or has directionally bounded variation. In this way, a unique characteristic can be singled out through each initial point. This approach yields the uniqueness of conservative solutions to various equations, including the Camassa-Holm and the variational wave equation u (tt) - c(u)(c(u)u (x) ) (x) = 0, for general initial data in H (1)(R).