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Symmetry analysis of a system of modified shallow-water equations
Institution:1. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke W., Montréal, QC H3A 2K6, Canada;2. Centre de recherches mathématiques, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, QC H3C 3J7, Canada;1. School of Mathematical Sciences, Shandong Normal University, Ji’nan 250014, PR China;2. Research Center on Logistics optimization and Prediction of Engineering Technology, Ji’nan, Shandong 250014, PR China;1. Universidade Nove de Julho, Departamento de Informática, Rua Guaranésia, n. 425, CEP 02112-000, São Paulo, SP, Brazil;2. Universidade Presbiteriana Mackenzie, Escola de Engenharia, Pós-Graduação em Engenharia Elétrica, Rua da Consolação, n. 896, CEP 01302-907, São Paulo, SP, Brazil;3. Universidade de São Paulo, Escola Politécnica, Departamento de Engenharia de Telecomunicações e Controle, Av. Prof. Luciano Gualberto, travessa 3, n. 380, CEP 05508-900, São Paulo, SP, Brazil;1. Macedonian Academy of Sciences and Arts, Skopje, Macedonia;2. BioCircuits Institute, University of California, San Diego, La Jolla, CA 92093-0402, USA;1. State Key Laboratory of Information Photonics and Optical Communications and School of Science, Beijing 100876, China;2. School of Communication and Electronics, Qingdao Technological University, Qingdao 266033, China;1. Dpto. de Matemática Aplicada, ESCET, Universidad Rey Juan Carlos, C/Tulipán s/n, 28933 Móstoles, Madrid, Spain;2. Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
Abstract:We revise the symmetry analysis of a modified system of one-dimensional shallow-water equations (MSWE) recently considered by Raja Sekhar and Sharma Commun Nonlinear Sci Numer Simulat 2012;20:630–36]. Only a finite dimensional subalgebra of the maximal Lie invariance algebra of the MSWE, which in fact is infinite dimensional, was found in the aforementioned paper. The MSWE can be linearized using a hodograph transformation. An optimal list of inequivalent one-dimensional subalgebras of the maximal Lie invariance algebra is constructed and used for Lie reductions. Non-Lie solutions are found from solutions of the linearized MSWE.
Keywords:Lie symmetries  Lie reductions  Exact solutions  Modified shallow-water equations  Hodograph transformation
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