  This paper develops methods for simplifying systems of partial differential
equations that have families of conservation laws which depend on functions of
the independent or dependent variables. In some cases, such methods can be
combined with reduction using families of symmetries, giving a multiple
reduction that is analogous to the double reduction of order for ordinary
differential equations with variational symmetries. Applications are given,
including a widely-used class of pseudoparabolic equations and several mean
curvature equations.
