| Summary: | The main concern of this paper is to investigate the various of interaction solutions to the (2+1)-dimensional variable-coefficient Sawada–Kotera equation. Analytical one-, two-, three- and four-soliton solutions of this equation are constructed based on its Hirota bilinear form. Through granting appropriate parameters and coefficients, special cases lead to resonance X-type soliton, S-type, U-type or periodic-type soliton solutions. The interaction solutions of multiple line solitons, between S-type line soliton and breather, U-type or S-type line soliton and lump wave, two U-type or S-type or periodic-type breathers, two S-type lump waves, among U-type or S-type two line solitons and one lump are obtained analytically, and some figures are provided with a better understanding of the dynamic behavior. We are confident that the results obtained in this paper are novel, which may be helpful to study other higher-dimensional nonlinear evolution equations
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