The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem
The Lax pairs of the higher-order Gerdjikov–Ivanov (HOGI) equation are extended to the multi-component formula. Then, we first derive four different types of nonlocal group reductions to this new system. To construct the solution of these four nonlocal equations, we utilize the Riemann–Hilbert metho...
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| Format: | Article |
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MDPI AG
2024-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/3/177 |
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| author | Jinshan Liu Huanhe Dong Yong Fang Yong Zhang |
| author_facet | Jinshan Liu Huanhe Dong Yong Fang Yong Zhang |
| author_sort | Jinshan Liu |
| collection | DOAJ |
| description | The Lax pairs of the higher-order Gerdjikov–Ivanov (HOGI) equation are extended to the multi-component formula. Then, we first derive four different types of nonlocal group reductions to this new system. To construct the solution of these four nonlocal equations, we utilize the Riemann–Hilbert method. Compared to the local HOGI equation, the solutions of nonlocal equations not only depend on the local spatial and time variables, but also the nonlocal variables. To exhibit the dynamic behavior, we consider the reverse-spacetime multi-component HOGI equation and its Riemann–Hilbert problem. When the Riemann–Hilbert problem is regular, the integral form solution can be given. Conversely, the exact solutions can be obtained explicitly. Finally, as concrete examples, the periodic solutions of the two-component nonlocal HOGI equation are given, which is different from the local equation. |
| first_indexed | 2024-04-24T18:16:03Z |
| format | Article |
| id | doaj.art-a50c22d7221246dd9d90136ef8b04236 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-04-24T18:16:03Z |
| publishDate | 2024-03-01 |
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| series | Fractal and Fractional |
| spelling | doaj.art-a50c22d7221246dd9d90136ef8b042362024-03-27T13:42:09ZengMDPI AGFractal and Fractional2504-31102024-03-018317710.3390/fractalfract8030177The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert ProblemJinshan Liu0Huanhe Dong1Yong Fang2Yong Zhang3College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThe Lax pairs of the higher-order Gerdjikov–Ivanov (HOGI) equation are extended to the multi-component formula. Then, we first derive four different types of nonlocal group reductions to this new system. To construct the solution of these four nonlocal equations, we utilize the Riemann–Hilbert method. Compared to the local HOGI equation, the solutions of nonlocal equations not only depend on the local spatial and time variables, but also the nonlocal variables. To exhibit the dynamic behavior, we consider the reverse-spacetime multi-component HOGI equation and its Riemann–Hilbert problem. When the Riemann–Hilbert problem is regular, the integral form solution can be given. Conversely, the exact solutions can be obtained explicitly. Finally, as concrete examples, the periodic solutions of the two-component nonlocal HOGI equation are given, which is different from the local equation.https://www.mdpi.com/2504-3110/8/3/177four nonlocal HOGI equationsnonlocal group reductionRiemann–Hilbert methodexact solution |
| spellingShingle | Jinshan Liu Huanhe Dong Yong Fang Yong Zhang The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem Fractal and Fractional four nonlocal HOGI equations nonlocal group reduction Riemann–Hilbert method exact solution |
| title | The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem |
| title_full | The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem |
| title_fullStr | The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem |
| title_full_unstemmed | The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem |
| title_short | The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem |
| title_sort | soliton solutions for nonlocal multi component higher order gerdjikov ivanov equation via riemann hilbert problem |
| topic | four nonlocal HOGI equations nonlocal group reduction Riemann–Hilbert method exact solution |
| url | https://www.mdpi.com/2504-3110/8/3/177 |
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