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<p>By using the Singular Manifold Method (SMM), this work analyzes the (3 + 1)-dimensional conformable fractional Wazwaz–Benjamin–Bona–Mahony (FWBBM) equation, which represents nonlinear low-amplitude wave propagation. The controlling partial differential equation is reduced to a nonlinear ordinary differential equation by means of a fractional traveling-wave transformation. Most importantly, Painlevé study guarantees equation integrability, therefore enabling the SMM application. The related Bäcklund transformation and the Schwarzian derivative for the eigenfunction are effectively obtained from the inquiry. Depending on certain parameter circumstances, this methodical methodology produces unique, precise complex traveling-wave solutions expressed in several analytical forms (including rational, trigonometric, and hyperbolic forms). 3D graphs help one to visualize the dynamic qualities of representative solutions. These results highlight the power and efficiency of the SMM for nonlinear fractional partial differential equation analysis and provide fresh analytical perspectives important for comprehending events such as ion-acoustic waves in plasma physics.</p>

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New insights into the (3 + 1)-dimensional Wazwaz–BBM wave equation via singular and fractional analysis

  • 期刊论文

  • 发表日期：

    2025年5月23日

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  • Ehab M. Almetwally,
  • Samah M. Mabrouk,
  • Ahmed S. Rashed,
  • Rasha Saleh

摘要

By using the Singular Manifold Method (SMM), this work analyzes the (3 + 1)-dimensional conformable fractional Wazwaz–Benjamin–Bona–Mahony (FWBBM) equation, which represents nonlinear low-amplitude wave propagation. The controlling partial differential equation is reduced to a nonlinear ordinary differential equation by means of a fractional traveling-wave transformation. Most importantly, Painlevé study guarantees equation integrability, therefore enabling the SMM application. The related Bäcklund transformation and the Schwarzian derivative for the eigenfunction are effectively obtained from the inquiry. Depending on certain parameter circumstances, this methodical methodology produces unique, precise complex traveling-wave solutions expressed in several analytical forms (including rational, trigonometric, and hyperbolic forms). 3D graphs help one to visualize the dynamic qualities of representative solutions. These results highlight the power and efficiency of the SMM for nonlinear fractional partial differential equation analysis and provide fresh analytical perspectives important for comprehending events such as ion-acoustic waves in plasma physics.