Abstract
By the symbolic computation and Hirota method, the bilinear form and an auto-Bäcklund transformation for a variable-coefficient Korteweg-de Vries equation with nonuniformities are given. Then, the N-solitonic solution in terms of Wronskian form is obtained and verified. In addition, it is shown that the (N – 1)- and N-solitonic solutions satisfy the auto-Bäcklund transformation through the Wronskian technique.
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