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<p>In this paper, the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation is investigated. The unified method, the modified Kudryashov scheme and the extended modified auxiliary equation mapping technique are employed to construct a variety of some new exact traveling wave solutions to the higher dimensional nonlinear model. Further, stability analysis and bifurcation analysis are employed to comprehend the dynamical system. Moreover, the physical structures of the observed solutions are demonstrated graphically. Via choosing appropriate amounts for the parameters contained in the obtained solutions, 3D plots, 2D contour plots and line plots are shown to graphically demonstrate the data. The reported results will be constructive in designing novel and better optical devices. The results of this work may also be useful in solving problems in marine engineering and nonlinear sciences.</p>

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On the structure of the higher dimensional Date-Jimbo-Kashiwara-Miwa model emerging in water waves

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月31日

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  • Kalim U. Tariq,
  • Jalil Manafian,
  • Somaye Malmir,
  • R. Nadir Tufail,
  • Onur Alp Ilhan,
  • Khaled H. Mahmoud

摘要

In this paper, the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation is investigated. The unified method, the modified Kudryashov scheme and the extended modified auxiliary equation mapping technique are employed to construct a variety of some new exact traveling wave solutions to the higher dimensional nonlinear model. Further, stability analysis and bifurcation analysis are employed to comprehend the dynamical system. Moreover, the physical structures of the observed solutions are demonstrated graphically. Via choosing appropriate amounts for the parameters contained in the obtained solutions, 3D plots, 2D contour plots and line plots are shown to graphically demonstrate the data. The reported results will be constructive in designing novel and better optical devices. The results of this work may also be useful in solving problems in marine engineering and nonlinear sciences.