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This paper is concerned with the stability of the rarefaction wave for the Burgers equation{ ut+f(u)x=μtαuxx, μ＞0, x∈R, t＞0, (Ⅰ)u|t=o = u0(x) →u± , x →∞ ,where 0 ≤α＜ 1/4q (q is determined by (2.2)). Roughly speaking, under the assumption that u- ＜ u+