Classification of Self Similar Solutions to a Generalized Burgers Equation

✍ Scribed by E. Soewono; L. Debnath

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 315 KB
• Volume: 184
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1994.1208

✦ Synopsis

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}) is obtained. The result gives an analytic justification to the result of Sachdev, Nair, and Tikekar [3] obtained through numerical and linear analysis. We also show the type of decay of the solutions at (\pm \infty) and the existence of periodic solutions if and only if (N=-1) and (\beta=r / s) where (r) and (s) are odd. 1994 Academic Press, Inc.