Abstract
In this paper, we introduce a new integrable nonlinear evolution equation in $$4+1$$ dimensions, which is an extension of Boiti–Leon–Manna–Pempinelli equation. We prove that this new equation has the Painleve property. By using the Bell polynomial approach, we obtain the bilinear representation, bilinear Backlund transformation, Lax pair and infinite conservation laws. Furthermore, several types of new exact solutions are also constructed based on the Hirota bilinear method, including the N-soliton solutions, periodic soliton solutions and mixed lump–kink wave solutions. The dynamics and interactions of localized wave solutions are illustrated by some graphs.
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