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Modulation instability characteristics for the higher-order modified derivative nonlinear Schrödinger equation: Cascading mechanism

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  • Zhang, Xi
  • Tang, Yaning
  • Yin, Huimin

Abstract

The higher-order modified derivative nonlinear Schrödinger equation is investigated in this paper. Through linear stability analysis, the modulation instability gain depending on the background parameters is obtained. The cascading instability mechanism in multimode perturbation evolution is elucidated. Different harmonics approximately intersect at a point which predicts nonlinear saturation and breather formation in Fermi–Pasta–Ulam–Tsingou recurrence. Furthermore, a quantitative correspondence is established between the modulation instability and fundamental nonlinear waves. Finally, numerical simulations are employed for the robustness of solutions, specifically, demonstrating instability of the propagation direction of breathers under perturbations. For the robustness test, the perturbation amplitude plays dominant role in triggering subsequent instabilities. These results provide theoretical insights for understanding and controlling wave dynamics in high-order nonlinear systems.

Suggested Citation

  • Zhang, Xi & Tang, Yaning & Yin, Huimin, 2026. "Modulation instability characteristics for the higher-order modified derivative nonlinear Schrödinger equation: Cascading mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 208(P3).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p3:s0960077926004480
    DOI: 10.1016/j.chaos.2026.118307
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