Abstract
A new type of variable separation solutions for the (2+1)-dimensional Korteweg–de Vries equation is derived by means of an improved mapping approach. The lump solutions are constructed and the interaction phenomena between a lump wave and muliti-kink waves are discussed, and some of these solutions exhibit a rich dynamics, with a wide variety of qualitative behavior and structures that are exponentially localized, showing some novel features and interesting behaviors.
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