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http://hdl.handle.net/2074/279
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| Title: | Similarity reductions and painleve analysis for the nonlinear boltzmann equation |
| Authors: | Vijayakumar, K
Bhutani, O P |
| Keywords: | Boltzmann equation
similarity reduction
Painleve analysis
symmetry operators |
| Issue Date: | 1996 |
| Publisher: | Elsevier Science |
| Citation: | Int. J. Engng Sci. 34, ( 5 ) 501-507 |
| Abstract: | Using scale invariant transformation we have obtained a new class of exact solution to the
Boltzmann equation of order (p + 1). Further, computation of symmetry operators for Boltzmann
equations of orders 2, 3, 4 and 5 has enabled us to conjecture the symmetry operator for all p ~ 1 + which leads to a Lie algebra of order 4. For p = 1, which corresponds to the Krook-Wu model of the Boltzmann equation, the resulting equation has been studied for group invariant solutions through similarity reduction and Painleve analysis. It is interesting to point out that Painleve analysis has, beside providing three new exact solutions to the Boltzmann equation, enabled us to recover two well
known solutions available earlier in the literature. |
| URI: | http://eprint.iitd.ac.in/dspace/handle/2074/279 |
| Appears in Collections: | Mathematics
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| vijaysim96.pdf | | 353Kb | Adobe PDF | View/Open |
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