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In this paper, a $$(3+1)$$(3+1)-dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund transformation is then presented, which consists of six… Click to show full abstract
In this paper, a $$(3+1)$$(3+1)-dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund 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 $$y=x$$y=x and $$y=z$$y=z are both derived. Finally, some figures are given to reveal the propagation of multiple wave solutions and lump solutions.
Journal Title: Nonlinear Dynamics
Year Published: 2017
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