| Abstract: |
| In this paper, we first obtain a bilinear form with small perturbation $u_0$ for the (4+1)-dimensional Fokas equation by an appropriate transformation. By using the Hirota bilinear operator, we construct the bilinear B\{a}cklund transformation which consists of three bilinear equations and involves four arbitrary parameters and then obtain a new class of lump solution including some free parameters for the (4+1)-dimensional Fokas equation based on the bilinear forms. By choosing different values of the parameters, the dynamic properties of six different cases of the lump solution are shown graphically. From the graphs, we can see some interesting nonlinear phenomena which might provide us with useful information on the dynamics of relevant fields in nonlinear science. Finally, we analyze the mathematical reasons of the lump solution by using the extreme value theory under the above six cases. |
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