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A generalized Sawada-Kotera equation and its Lax pairs are proposed. With the help of the gauge transformation between spectral problems, a Darboux transformation for the generalized SK equation is constructed. As an application of the Darboux transformation, we give some explicit solutions of the generalized SK equation such as the rational solutions, soliton solutions, and periodic solutions.

Darboux Transformation and Explicit Solutions for a Generalized Sawada-Kotera Equation