On quasi-periodic wave solutions and asymptotic behaviors to a (2+1)-dimensional generalized variable-coefficient Sawada-Kotera equation

In this paper, a (2 + 1)-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.