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A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method
Author(s) -
ElSayed M. F.,
Moatimid G. M.,
Moussa M. H. M.,
ElShiekh R. M.,
ElShiekh F. A. H.,
ElSatar A. A.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3307
Subject(s) - mathematics , boltzmann equation , homogeneous space , lie algebra , mathematical physics , boltzmann constant , lie group , lattice boltzmann methods , burgers' equation , nonlinear system , symmetry (geometry) , infinitesimal , algebra over a field , mathematical analysis , pure mathematics , partial differential equation , physics , quantum mechanics , geometry
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.