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<p>Dispersionless models play a significant role in describing short-wave and ultrashort-pulse phenomena in nonlinear media, also in the geometric-optics limit of integrable systems. The nonlocal complex coupled dispersionless system in particular, offers a mathematically tractable setting for examining nonlinear interactions such as kinks, breathers, and mixed structures generated through binary Darboux transformations. We construct a binary Darboux transformation for the nonlocal complex coupled dispersionless system and obtain quasi-Grammian breather–kink interactions. These findings reveal the coexistence of symmetry-preserving and breaking solutions within complex coupled dispersionless systems. To further substantiate these theoretical results, the solution dynamics are illustrated through surface and contour plots, providing a visual representation of their behavior.</p>

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Symmetry-Breaking and Preserving Breather, Kink interactions of Nonlocal Complex-Coupled Dispersionless Equation

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Zeeshan Amjad,
  • A. Eid,
  • Aamir Farooq,
  • Faisal Javed,
  • Tajamal Mazhar,
  • N. Mustapha

摘要

Dispersionless models play a significant role in describing short-wave and ultrashort-pulse phenomena in nonlinear media, also in the geometric-optics limit of integrable systems. The nonlocal complex coupled dispersionless system in particular, offers a mathematically tractable setting for examining nonlinear interactions such as kinks, breathers, and mixed structures generated through binary Darboux transformations. We construct a binary Darboux transformation for the nonlocal complex coupled dispersionless system and obtain quasi-Grammian breather–kink interactions. These findings reveal the coexistence of symmetry-preserving and breaking solutions within complex coupled dispersionless systems. To further substantiate these theoretical results, the solution dynamics are illustrated through surface and contour plots, providing a visual representation of their behavior.