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<p>In quantum and fluid mechanics, nonlinear models are reported, including a (3+1)-dimensional generalized variable-coefficient Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation describing the interaction between a long wave and a Riemann wave, which is the subject of this paper. For that equation, we find (A) a bilinear form, (B) a set of the bilinear auto-Bäcklund transformations with some soliton solutions and (C) a set of the similarity reductions. Our results, i.e., bilinear form, bilinear auto-Bäcklund transformations with solitons as well as similarity reductions, may help people investigate certain wave modes and dynamic features in quantum and fluid mechanics in the future.</p>

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Bilinear Forms, Bilinear Auto-Bäcklund Transformations and Similarity Reductions for a (3+1)-Dimensional Generalized Variable-Coefficient Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff Equation in Quantum and Fluid Mechanics

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Xin-Yi Gao,
  • Wei-Gang Zhao,
  • Da-Wei Zuo

摘要

In quantum and fluid mechanics, nonlinear models are reported, including a (3+1)-dimensional generalized variable-coefficient Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation describing the interaction between a long wave and a Riemann wave, which is the subject of this paper. For that equation, we find (A) a bilinear form, (B) a set of the bilinear auto-Bäcklund transformations with some soliton solutions and (C) a set of the similarity reductions. Our results, i.e., bilinear form, bilinear auto-Bäcklund transformations with solitons as well as similarity reductions, may help people investigate certain wave modes and dynamic features in quantum and fluid mechanics in the future.