Title

Classification of Self Similar Solutions to a Generalized Burgers Equation

Abstract

A complete classification for the self-similar solutions to the generalized Burgers equation ut+uβux=tNuxx of the form u(t, η)=A1t-(1-N)/2βF(η), where η=A2xt-(1+N)/2, [formula], and A1=(2A2)-1/β 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 ±∞ and the existence of periodic solutions if and only if N=-1 and β=r/s where r and s are odd. © 1994 Academic Press, Inc.

Publication Date

6-1-1994

Publication Title

Journal of Mathematical Analysis and Applications

Volume

184

Issue

2

Number of Pages

389-398

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1006/jmaa.1994.1208

Socpus ID

0005245462 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0005245462

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