  An effective algorithmic method is presented for finding the local
conservation laws for partial differential equations with any number of
independent and dependent variables. The method does not require the use or
existence of a variational principle and reduces the calculation of
conservation laws to solving a system of linear determining equations similar
to that for finding symmetries. An explicit construction formula is derived
which yields a conservation law for each solution of the determining system. In
the first of two papers (Part I), examples of nonlinear wave equations are used
to exhibit the method. Classification results for conservation laws of these
equations are obtained. In a second paper (Part II), a general treatment of the
method is given.
