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<p>This investigation addresses the nonlinear Tzitzeica–Dodd–Bullough (TDB) equation, a paradigmatic model in nonlinear science distinguished by mixed second-order derivatives and exponential nonlinearities. The TDB framework possesses substantial physical relevance, arising in quantum field theory, solid-state dynamics, nonlinear optics, and the modeling of electromagnetic wave propagation. To construct rigorous solutions, two symbolic methodologies–the Khater II (Khat II) approach and a modified Kudryashov (MKud) scheme–are employed, yielding closed-form expressions that faithfully represent the interplay between nonlinearity and spatiotemporal dispersion. In parallel, He’s variational iteration (HVI) method is utilized as a high-fidelity numerical benchmark, providing independent validation of the symbolic results through excellent concordance. This concordance affirms both the accuracy of the derived wave structures and the robustness of the underlying mathematical techniques, with particular emphasis on the stability and morphology of coherent dynamical profiles. The novelty of this study is threefold: the selection of a mathematically rich and underexplored nonlinear model, the integration of complementary analytical and semi-analytical methods, and the refined insight it offers into nonlinear wave behavior in continuous media. Collectively, the results contribute substantively to the ongoing development of formal solution strategies for nonlinear partial differential equations, offering a theoretical foundation for future explorations in applied mathematics and mathematical physics.</p>

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Interplay between medium-induced nonlinearity and wave propagation characteristics: the nonlinear Tzitaeica–Dodd–Bullough model in nonlinear optics and electromagnetic waves

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Mostafa M. A. Khater,
  • Saud Owyed

摘要

This investigation addresses the nonlinear Tzitzeica–Dodd–Bullough (TDB) equation, a paradigmatic model in nonlinear science distinguished by mixed second-order derivatives and exponential nonlinearities. The TDB framework possesses substantial physical relevance, arising in quantum field theory, solid-state dynamics, nonlinear optics, and the modeling of electromagnetic wave propagation. To construct rigorous solutions, two symbolic methodologies–the Khater II (Khat II) approach and a modified Kudryashov (MKud) scheme–are employed, yielding closed-form expressions that faithfully represent the interplay between nonlinearity and spatiotemporal dispersion. In parallel, He’s variational iteration (HVI) method is utilized as a high-fidelity numerical benchmark, providing independent validation of the symbolic results through excellent concordance. This concordance affirms both the accuracy of the derived wave structures and the robustness of the underlying mathematical techniques, with particular emphasis on the stability and morphology of coherent dynamical profiles. The novelty of this study is threefold: the selection of a mathematically rich and underexplored nonlinear model, the integration of complementary analytical and semi-analytical methods, and the refined insight it offers into nonlinear wave behavior in continuous media. Collectively, the results contribute substantively to the ongoing development of formal solution strategies for nonlinear partial differential equations, offering a theoretical foundation for future explorations in applied mathematics and mathematical physics.