This research reveals soliton solutions for the two-component gerdjikov–ivanov equation, suggesting new insights into multicomponent integrable systems.
This paper investigates the two‐component Gerdjikov–Ivanov equation through a matrix ‐problem with two linear constraints. First, we derive the spatial and time spectral problems of the two‐component Gerdjikov–Ivanov equation. Second, we rigorously establish the gauge equivalence between the spatial spectral problems of the two‐component Gerdjikov–Ivanov equation and the Sasa–Satsuma equations under specific conditions. Finally, by analyzing discrete spectral configurations, we construct multiple types of soliton solutions for the two‐component Gerdjikov–Ivanov equation using the ‐dressing method. The results demonstrate the effectiveness of this method in studying multicomponent integrable systems.
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Wang et al. (2025) studied this question.
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