Conservation laws by means of a new mixed method |
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| Affiliation: | 1. Faculty of Engineering and Architecture, Kore University of Enna, Via delle Olimpiadi, Cittadella Universitaria, I-94100, Enna, Italy;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;1. School of Mathematical Sciences, Beihang University, 100191 Beijing, China;2. Academy of Mathematics & Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;1. Université Bordeaux, Institut de Mathématiques de Bordeaux, F-33405 Talence Cedex, France;2. Academy of Mathematics & Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, The Chinese Academy of Sciences, Beijing 100190, China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;4. School of Mathematical Science, Peking University, Beijing 100871, China |
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| Abstract: | In this paper, by using a mixed approach, recently introduced by the authors, some conservation laws of partial differential equations are derived. The method merges the Ibragimov’s method and the one by Anco and Bluman. In particular, by applying this new mixed method, we determine all zero-th order conservation laws of Chaplygin and Shallow Water equations, as well as new conservation laws for a second order partial differential equation involving an arbitrary function. |
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| Keywords: | Conservation laws Lie point symmetries Differential equations |
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