Geodesic
Darboux transformation and exact solutions of the~variable-coefficient nonlocal Gerdjikov--Ivanov equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 1, pp. 23-36

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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.
Mots-clés : variable-coefficient nonlocal Gerdjikov–Ivanov equation, Darboux transformation, exact solution. 
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     author = {Yuru Hu and Feng Zhang and Xiangpeng Xin and Hanze Liu},
     title = {Darboux transformation and exact solutions of the~variable-coefficient nonlocal {Gerdjikov--Ivanov} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {23--36},
     publisher = {mathdoc},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_1_a1/}
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Yuru Hu; Feng Zhang; Xiangpeng Xin; Hanze Liu. Darboux transformation and exact solutions of the~variable-coefficient nonlocal Gerdjikov--Ivanov equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 1, pp. 23-36. http://geodesic.mathdoc.fr/item/TMF_2022_211_1_a1/