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<p>The Boussinesq equation describes the interaction of shallow water waves and also plays a crucial role in many fields of physics. In this paper, a new extended (3+1)-dimensional Boussinesq equation is studied. The integrability of the equation is verified by Painlevé analysis, and the bilinear auto-Bäcklund transformation, multiple soliton solutions and soliton molecules of the equation are derived by Hirota bilinear method. The traveling wave solutions of this equation are constructed by modified auxiliary equation method. These exact solutions are also shown graphically. Our results are helpful for understanding nonlinear wave phenomena. </p>

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Painlevé Integrability, Auto-Bäcklund Transformation and Exact Solutions of an Extended (3+1)-Dimensional Boussinesq Equation

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Saifeng Li,
  • Lianzhong Li

摘要

The Boussinesq equation describes the interaction of shallow water waves and also plays a crucial role in many fields of physics. In this paper, a new extended (3+1)-dimensional Boussinesq equation is studied. The integrability of the equation is verified by Painlevé analysis, and the bilinear auto-Bäcklund transformation, multiple soliton solutions and soliton molecules of the equation are derived by Hirota bilinear method. The traveling wave solutions of this equation are constructed by modified auxiliary equation method. These exact solutions are also shown graphically. Our results are helpful for understanding nonlinear wave phenomena.