2021/05/18 by Jinyan Zhu, JinYan Zhu, Yong Chen +2 · 1 citation
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.48550/arxiv.2105.08412
arxiv created 2021/05/18 · openalex publication_date 2021/05/18 · arxiv updated 2021/05/19 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28
The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in this paper, we mainly consider the third-order flow GI equation. In the framework of the Riemann-Hilbert method, through a standard dressing procedure, soliton matrices for simple zeros and elementary high-order zeros in the Riemann-Hilbert problem (RHP) for the third-order flow GI equation are constructed. Taking advantage of this result, some properties and asymptotic analysis of single soliton solutions and two-soliton solutions are discussed, and the simple elastic interaction of two-soliton is proved. Compared with soliton solution of the classical second-order flow, we found that the higher-order dispersion term affects the propagation velocity, propagation direction and amplitude of the soliton. Finally, by means of certain limit technique, the high-order soliton solution matrix for the third-order flow GI equation is derived.