Abstract
In this paper, a [Formula: see text]-dimensional generalized variable-coefficient Sawada–Kotera (gvcSK) equation is investigated, which describes many nonlinear phenomena in fluid dynamics and plasma physics. Based on the properties of binary Bell polynomials, we present a Hirota’s bilinear equation to the gvcSK equation. By virtue of the Hirota’s bilinear equation, we obtain the N-soliton solutions and the quasi-periodic wave solutions of the gvcSK equation, which can be reduced to the ones of several integrable equations such as Sawada–Kotera, modified Caudrey–Dodd–Gibbon–Sawada–Kotera, isospectral BKP equations and etc. Furthermore, we obtain the relationship between the soliton solutions and periodic solutions by considering the asymptotic properties of the periodic solutions.
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