A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method |
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| Authors: | M. F. El‐Sayed G. M. Moatimid M. H. M. Moussa R. M. El‐Shiekh F. A. H. El‐Shiekh A. A. El‐Satar |
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| Affiliation: | 1. Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Heliopolis, Cairo, Egypt;2. Department of Mathematics, Faculty of girls, Jazan University, Saudi Arabia |
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| Abstract: | In this paper,we applied the Painlevé property test on Krook‐Wu model of the nonlinear Boltzmann equation (p = 1). As a result, by using Bäcklund transformation, we obtained three solutions two of them were known earlier, while the third one is new and more general, we have also two reductions one of them is Abel's equation. Also, Lie‐group method is applied to the (p + 1)th Boltzmann equation. The complete Lie algebra of infinitesimal symmetries is established. Three nonequivalent sub‐algebraic of the complete Lie algebra are used to investigate similarity solutions and similarity reductions in the form of nonlinear ordinary equations for (p + 1)th Boltzmann equation; we obtained two general solutions for (p + 1)th Boltzmann equation and new solutions for Krook‐Wu model of Boltzmann equation (p = 1). Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | painleve analysis Lie‐Group method |
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