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For CH-γ equation ut+c0ux+3uux-α(uxxt+uuxxx+2uxuxx)=-γuxxx;in order to extend the peakon solutions,we choose α and γ as bifurcation parameters to make qual-itative analysis. By using bifurcation method of phase portraits,We obtained some new expressions of peakons. And then the properties about other traveling wave solutions converging to peakons are summarized as corresponding theorems.