The \((4+1)\)-dimensional Fokas (4DFK) equation is explicitly written out by means of the linearized operator of the 4DFK equation after introducing an additional auxiliary variable. Based on the bilinear form, bilinear Bäcklund transformations consisting of three bilinear equations are provided. A new class of lump solutions is given and analyzed using the extremum theory of multivariate function, of which the peculiar dynamic property is demonstrated graphically.

中文翻译：

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$$（4 + 1）$$（4 +1）维Fokas方程的集总解和双线性Bäcklund变换

的\（（4 + 1）\）维Fokas的（4DFK）方程由4DFK方程的引入附加辅助变量后的线性化操作者的手段明确地写出。基于双线性形式，提供了由三个双线性方程组成的双线性Bäcklund变换。使用多元函数的极值理论给出并分析了一类新的总解，并通过图形展示了其独特的动力学性质。