The association of non-local symmetries with conservation laws: applications to the heat and Burger’s equations

摘要

We extend the definition of the association of symmetries of partial differential equations with conservation laws to the non-local case. It is shown that if a conservation law is associated to a symmetry, a part of its equivalence class is also associated to that symmetry. Applications to the linear heat equation, the potential Burger’s equation and Burger’s equation are given.