arXiv:1612.04859v1 [math-ph] 14 Dec 2016 On the construction of conservation laws: a mixed approach M. Ruggieri 1 , M. P. Speciale 2 1 Faculty of Engineering and Architecture, Kore University of Enna Via delle Olimpiadi, Cittadella Universitaria, I–94100, Enna, Italy Email: marianna.ruggieri@unikore.it 2 Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina Viale F. Stagno d’Alcontres 31, I–98166 Messina, Italy Email: mpspeciale@unime.it Abstract A new approach, combining the Ibragimov method and the one by Anco and Bluman, with the aim of algorithmically computing local conservation laws of partial differential equations, is discussed. Some examples of the application of the procedure are given. The method, of course, is able to recover all the conservation laws found by using the direct method; at the same time we can characterize which symmetry, if any, is responsible for the existence of a given conservation law. Some new local conservation laws for the Short Pulse equation and for the Fornberg–Whitham equation are also determined. Keywords: Conservation laws, Lie point symmetries, a systematic procedure. 1 Introduction In dealing with differential equations, conservation laws have a deep rele- vance, since they often express the conservation of physical quantities. They 1