Direct similarity analysis of generalized burgers equations and perturbation solutions of Euler-Painleve transcendents

摘要

Similarity reductions of the generalized Burgers equation u(t) +u(n)u(x) + (j/2t + alpha)u + (beta + gamma/x)u(n+1) = u(xx), where alpha, beta, and gamma 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 x/roott, and to provide a perturbation solution of an Euler-Painleve transcedent. [References: 22]