| In this paper, I consider the traveling wave solutions and peakons of the generalized Camassa-Holm (GCH) equation and give the express of the solitons of this equation. The peakons and their figures of the GCH equation are given with the Mathematic software for m -1 , m = 2 and m = 3 in particular ; For m=3, I get the generalized dissipative Camassa-Holm equations by adding a dissipative term and find two types exact traveling wave solutions of this equations. I also apply the homogeneous balance method into the GCH equation so that I get a group of smooth solutions for m = 2 and m = 3 and the Backlund transformation for m - 3 of the GCH equation.
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