Advances in Mathematical Physics (Jan 2024)

New Multilinear Variable Separation Solutions of the (3 + 1)-Dimensional Burgers Hierarchy

  • Wei Zhu,
  • Jian-Yong Wang,
  • Kai Zhou,
  • Shoufeng Shen,
  • Bo Ren

DOI
https://doi.org/10.1155/2024/5533472
Journal volume & issue
Vol. 2024

Abstract

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The multilinear variable separation (MLVS) approach has been proven to be very useful in solving (2 + 1)-dimensional integrable systems. Taking the (3 + 1)-dimensional Burgers hierarchy as an example, we extend the MLVS approach to a whole family of (3 + 1)-dimensional Burgers hierarchy. New exact solutions and universal formulas are obtained, which lead to abundant (3 + 1)-dimensional coherent structures. In particular, two ring-type soliton molecules and their interactions are shown in detail. We also generalize the MLVS results of the (3 + 1)-dimensional Jimbo–Miwa (JM) equation and modified JM equation.