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<p>The B-type Kadomtsev-Petviashvili (BKP) equation is commonly employed to depict the propagation of long waves in shallow water, and is widely used in optics, plasma physics, and water waves. In the present work, we introduce a new extended (3+1)-dimensional BKP equation. Initially, the integrability of the equation is examined using Painlevé analysis. Then we acquire a bilinear auto-Bäcklund transformation, multiple soliton solutions as well as the soliton molecules of the equation, and show the dynamical behaviors via 3D and projection figures. Furthermore, employing the generalized Riccati equation mapping method, numerous explicit and generalized solitary wave solutions are derived. Finally, the stability of the considered equation is discussed with the help of linear stability technique. Our results are helpful for understanding nonlinear phenomena.</p>

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Painlevé integrability, exact solutions and stability analysis for a new extended (3+1)-dimensional BKP equation

  • 期刊论文

  • 发表日期：

    2025年4月28日

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  • Jie Huang,
  • Lianzhong Li

摘要

The B-type Kadomtsev-Petviashvili (BKP) equation is commonly employed to depict the propagation of long waves in shallow water, and is widely used in optics, plasma physics, and water waves. In the present work, we introduce a new extended (3+1)-dimensional BKP equation. Initially, the integrability of the equation is examined using Painlevé analysis. Then we acquire a bilinear auto-Bäcklund transformation, multiple soliton solutions as well as the soliton molecules of the equation, and show the dynamical behaviors via 3D and projection figures. Furthermore, employing the generalized Riccati equation mapping method, numerous explicit and generalized solitary wave solutions are derived. Finally, the stability of the considered equation is discussed with the help of linear stability technique. Our results are helpful for understanding nonlinear phenomena.