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<p>Our goal is to study the (2 + 1) sinh-Gordon equation’s generalization with a <i>q</i>-deformation parameter. This equation describes systems with violated symmetries. By introducing noncommutativity and non-linearity, the <i>q</i>-deformed version expands upon the traditional sinhGordon equation. We investigate two approaches for solving this equation: the reduced <i>q</i>-differential transform method (R<i>q</i>DTM) and the variational iteration method (VIM). R<i>q</i>DTM is a modified version of the differential transform method designed for <i>q</i>-deformed equations, while VIM uses an iterative scheme. We compare the accuracy and efficiency of the solutions obtained from these methods and present numerical results. This analysis helps us assess the strengths and weaknesses of each approach in solving the (2 + 1) <i>q</i>-deformed sinh-Gordon equation, providing valuable insights into their applicability and performance.</p>

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Unraveling the complexity of q-deformed dynamics: a study of novel solutions and their implications for nonlinear phenomena

  • 期刊论文

  • 发表日期：

    2025年3月2日

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  • Zaki Mrzog Alaofi,
  • K. R. Raslan,
  • Ahmed S. Shehata,
  • Khalid K. Ali

摘要

Our goal is to study the (2 + 1) sinh-Gordon equation’s generalization with a q-deformation parameter. This equation describes systems with violated symmetries. By introducing noncommutativity and non-linearity, the q-deformed version expands upon the traditional sinhGordon equation. We investigate two approaches for solving this equation: the reduced q-differential transform method (RqDTM) and the variational iteration method (VIM). RqDTM is a modified version of the differential transform method designed for q-deformed equations, while VIM uses an iterative scheme. We compare the accuracy and efficiency of the solutions obtained from these methods and present numerical results. This analysis helps us assess the strengths and weaknesses of each approach in solving the (2 + 1) q-deformed sinh-Gordon equation, providing valuable insights into their applicability and performance.