Abstract
In this paper, we investigate a generalized (4 + 1)-dimensional variable-coefficient Fokas equation for the shallow water waves. Through the truncated Painlevé expansion, we give the auto-Bäcklund transformations. Based on the Hirota method, we get the two-soliton solutions. With different choices of certain variable coefficients, we observe some phenomena of the two solitons. We obtain the ring-type and periodic-type two solitons. In addition, we derive the resonant two solitons with the linear, hyperbolic, and periodic types.
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