Abstract
In this paper, under the Painlevé-integrable condition, the auto-Bäcklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painlevé expansion method, extended variable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painlevé expansion method and extended variable-coefficient balancing-act method is testified.
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