Generalization of the double reduction theory |
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Authors: | Ashfaque H Bokhari Ahmad Y Al-Dweik FD Zaman AH Kara FM Mahomed |
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Institution: | 1. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia;2. School of Mathematics, University of the Witwatersrand, Wits 2050, South Africa;3. School of Computation and Applied Mathematics, Center for Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Wits 2050, South Africa |
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Abstract: | In a recent work Sjöberg (2007, 2008) 1], 2] remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to find invariant solution for a non linear system of th order partial differential equations with independent and dependent variables provided that the non linear system of partial differential equations admits a nontrivial conserved form which has at least one associated symmetry in every reduction. In order to give an application of the procedure we apply it to the nonlinear (2+1) wave equation for arbitrary function and . |
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