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Self-similar solutions of the generalized Emden-Fowler equation

✍ Scribed by P.G.L. Leach; R. Maartens; S.D. Maharaj

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 477 KB
Volume: 27
Category: Article
ISSN: 0020-7462
DOI: 10.1016/0020-7462(92)90062-c

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A complete classification for the self-similar solutions to the generalized Burgers equation \[ u_{t}+u^{\beta} u_{x}=t^{N} u_{x x} \] of the form \(u(t, \eta)=A_{1} t^{-(1-N) / 2 \beta} F(\eta)\), where \(\eta=A_{2} x t^{-(1+N / 2}, A_{2}=1 / \sqrt{2 A}\), and \(A_{1}=\left(2 A_{2}\right)^{-1 / 6