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Direct Similarity Analysis of Generalized Burgers Equations and Perturbation Solutions of Euler–Painlevé Transcendents
Author(s) -
Mayil Vaganan B.,
Asokan R.
Publication year - 2003
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.t01-1-00041
Subject(s) - mathematics , perturbation (astronomy) , euler's formula , burgers' equation , similarity (geometry) , mathematical analysis , kruskal's algorithm , euler equations , pure mathematics , similarity solution , power function , mathematical physics , partial differential equation , combinatorics , physics , quantum mechanics , thermodynamics , artificial intelligence , computer science , image (mathematics) , boundary layer , spanning tree
Similarity reductions of the generalized Burgers equation , where α, β, and γ are non‐negative constants, n a positive integer and j = 0, 1, 2 , are obtained by the direct method of Clarkson and Kruskal [1]. This is the first work to report the similarity variables as an incomplete gamma function and also as a power of , and to provide a perturbation solution of an Euler–Painlevé transcedent.