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Periodic and decay mode solutions of the generalized variable-coefficient Korteweg–de Vries equation

In this paper, we can obtain periodic and decay mode solutions of the generalized variable-coefficient Korteweg–de Vries (gvc-KdV) equation for the first time by using the multivariate transformation technique. Periodic solutions are doubly and triply periodic solutions, and the decay mode solutions include the 1-decay solution and the 2-decay mode solution. Furthermore, we will also study the effect of variation of parameters for solutions systematically, relating to different forms of expression, through graphic display.