Abstract
In this paper, a $$(3+1)$$ -dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Backlund transformation is then presented, which consists of six bilinear equations and involves nine arbitrary parameters. With multiple exponential function method and symbolic computation, nonresonant-typed one-, two-, and three-wave solutions are obtained. Furthermore, two classes of lump solutions to the dimensionally reduced cases with $$y=x$$ and $$y=z$$ are both derived. Finally, some figures are given to reveal the propagation of multiple wave solutions and lump solutions.
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