Lump solutions and bilinear Bäcklund transformation for the \((4+1)\)-dimensional Fokas equation


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.

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The authors would like to thank the reviewers and editors for their suggestions and helpful comments on improving the paper.

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Correspondence to Ruoxia Yao or Yali Shen.

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Supported by the National Natural Science Foundation of China (11471004, 11501498), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2019L0868) and the Project of the Youth Fund of Shanxi (201901D211461)

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Yao, R., Shen, Y. & Li, Z. Lump solutions and bilinear Bäcklund transformation for the \((4+1)\)-dimensional Fokas equation. Math Sci (2020).

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  • \((4+1)\)-Dimensional Fokas equation
  • Bilinear form
  • Bilinear Bäcklund transformation
  • Lump solutions