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<p>We study a non-commutative coupled dispersionless system with spatially dependent coefficients, motivated by current-fed string models in external magnetic fields. Using a Lax pair formulation, we establish integrability and construct explicit solutions via iterative Darboux transformations and quasideterminants. The results highlight distinct nonlinear wave behaviors, including bright and dark solitons, curved and asymmetric trajectories, and oscillatory dynamics. Numerical simulations demonstrate how non-commutativity significantly influences soliton structure and stability in spatially inhomogeneous settings.</p>

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Exact solutions and nonlinear wave interactions in a non-commutative coupled dispersionless system with variable coefficients

  • 期刊论文

  • 发表日期：

    2025年9月23日

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  • H. W. A. Riaz,
  • A. Farooq

摘要

We study a non-commutative coupled dispersionless system with spatially dependent coefficients, motivated by current-fed string models in external magnetic fields. Using a Lax pair formulation, we establish integrability and construct explicit solutions via iterative Darboux transformations and quasideterminants. The results highlight distinct nonlinear wave behaviors, including bright and dark solitons, curved and asymmetric trajectories, and oscillatory dynamics. Numerical simulations demonstrate how non-commutativity significantly influences soliton structure and stability in spatially inhomogeneous settings.