Symmetries and nonlocal conservation laws of the general magma equation |
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| Authors: | Raisa Khamitova |
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| Institution: | 1. School of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China;2. State Key Laboratory of Ocean Engineering, School of Naval Architecture Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;3. Australian Research Council Centre of Excellence for Nanoscale BioPhotonics, School of Science, RMIT University, Melbourne, VIC 3001, Australia |
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| Abstract: | In this paper the general magma equation modelling a melt flow in the Earth’s mantle is discussed. Applying the new theorem on nonlocal conservation laws Ibragimov NH. A new conservation theorem. J Math Anal Appl 2007;333(1):311–28] and using the symmetries of the model equation nonlocal conservation laws are computed. In accordance with Ibragimov Ibragimov NH. Quasi-self-adjoint differential equations. Preprint in Archives of ALGA, vol. 4, BTH, Karlskrona, Sweden: Alga Publications; 2007. p. 55–60, ISSN: 1652-4934] it is shown that the general magma equation is quasi-self-adjoint for arbitrary m and n and self-adjoint for n = ?m. These important properties are used for deriving local conservation laws. |
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