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Darboux transformation and exact solutions of the variable-coefficient nonlocal Gerdjikov–Ivanov equation

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Abstract

We for the first time study the integrable nonlocal nonlinear Gerdjikov–Ivanov (GI) equation with variable coefficients. The variable-coefficient nonlocal GI equation is constructed using a Lax pair. On this basis, the Darboux transformation is studied. Exact solutions of the variable-coefficient nonlocal GI equation are then obtained by constructing the \(2n\)-fold Darboux transformation of the equation. The results show that the solution of the GI equation with variable coefficients is more general than that of its constant-coefficient form. By taking special values for the coefficient function, we can obtain specific exact solutions, such as a kink solution, a periodic solution, a breather solution, a two-soliton interaction solution, etc. The exact solutions are represented visually with the help of images.

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Funding

This work is supported by the National Natural Science Foundation of China (grant No. 11505090), Research Award Foundation for Outstanding Young Scientists of Shandong Province (grant No. BS2015SF009), and the Doctoral Foundation Of Liaocheng University (grant No. 318051413), Liaocheng University Level Science and Technology Research Fund (grant No. 318012018).

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Correspondence to Xiangpeng Xin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 211, pp. 23–36 https://doi.org/10.4213/tmf10183.

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Hu, Y., Zhang, F., Xin, X. et al. Darboux transformation and exact solutions of the variable-coefficient nonlocal Gerdjikov–Ivanov equation. Theor Math Phys 211, 460–472 (2022). https://doi.org/10.1134/S004057792204002X

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