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The dressing method based on the $2\times2$ matrix $\bar\partial$-problem isgeneralized to study the canonical form of AB equations. The soliton solutionsfor the AB equations are given by virtue of the properties of Cauchy matrix.Asymptotic behaviors of the $N$-soliton solution are discussed.

The AB equations and the $\bar\partial$-dressing method in semi-characteristic coordinates