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[en] We show that, under an irrotational condition, there exists an n-dimensional Hopf–Cole transformation between the n-dimensional Burgers system and an n-dimensional heat equation. Further, as application of the Hopf–Cole transformation, two kinds of physically interesting exact solutions for the n-dimensional Burgers equations are found. In the first kind of solutions, the velocity fields are topological solitons. In the second kind of solutions, velocity fields are all multiple fusion soliton solutions. - Highlights: • Find an irrotational condition to linearize n-dimensional Burgers system. • Generalize classical Hopf–Cole transformation to n-dimensional Burgers system. • Present topological solitons and multiple fusion soliton solutions.