| 基于Dbar 方法研究耦合Gerdjikov-Ivanov 方程的高阶孤子解 |
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| 引用本文：温丽丽.基于Dbar 方法研究耦合Gerdjikov-Ivanov 方程的高阶孤子解[J].上海第二工业大学(中文版),2026,43(1):89-96 |
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| 基金项目:上海市青年教师资助计划上海第二工业大学优秀教师启萌计划 (A01GY25F012) 资助 |
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| 中文摘要:Dbar 方法作为 Riemann-Hilbert方法与反散射理论的推广, 具有更广的适用性与更强的普适性, 从而在求解精确解时更具优势。本文基于 Dbar 方法研究耦合 Gerdjikov-Ivanov 方程的高阶孤子解, 有效获得了五阶以内的孤子解 qj (x, t) 和 rj (x, t)(j = 1, 2, · · · , 5), 并分析了其动力学行为。此外, 还刻画了 qj (x, t) 和 rj (x, t) 在不同时刻的演化轨迹。 |
| 中文关键词:Dbar 方法 耦合 Gerdjikov-Ivanov 方程 高阶孤子解 |
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| Study of Higher-Order Soliton Solutions for the Coupled Gerdjikov-Ivanov Equation Based on the Dbar Method |
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| Abstract:As a generalization of the Riemann-Hilbert method and the inverse scattering transform, the Dbar method possesses both broader applicability and greater generality, thereby offering an advantages in constructing exact solutions. Based on the Dbar method, higher-order soliton solutions of the coupled Gerdjikov-Ivanov equations are investigated. Explicit solutions up to the fifth order are successfully obtained, and the dynamic behaviors of the components qj (x, t) and rj (x, t)(j = 1, 2, · · · , 5) are analyzed. Furthermore, the spatial evolution of qj (x, t) and rj (x, t) is illustrated at different time instances. |
| keywords:Dbar method the coupled Gerdjikov-Ivanov equations high-order soliton solutions |
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