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.

Wei Zhu

Jian-Yong Wang

Kai Zhou

Shoufeng Shen

Bo Ren

Advances in Mathematical Physics

ADVANCES IN MATHEMATICAL PHYSICS 发表的论文旨在理解物理现象的数学基础，并通过数学方法解决物理问题。该杂志欢迎数学物理学家、理论物理学家和数学家的投稿。除了原创研究，《数学物理学进展》还发表重点评论文章，检查最新技术，确定新兴趋势，并为发展领域提出未来方向。

The papers published in Advances in Mathematical Physics aim to deepen the understanding of the mathematical foundations of physical phenomena and to solve physical problems through mathematical methods. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians. In addition to original research articles, Advances in Mathematical Physics also publishes review articles that examine the latest techniques, identify emerging trends, and propose future directions for the development of the field.

《Advances in Mathematical Physics》发表的论文旨在深入理解物理现象的数学基础，并通过数学方法解决相关的物理问题。该杂志欢迎数学物理学家、理论物理学家和数学家的投稿。除了原创研究文章外，《Advances in Mathematical Physics》还发表重点评论文章，探讨最新技术，识别新兴趋势，并为该领域的发展提出未来方向。

Category	Quartile
物理与天体物理	4
物理与天体物理, 物理数学物理	4

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

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