The Nonlinear Steepest Descent Approach for Long Time Behavior
          of the Two-component Coupled Sasa-Satsuma Equation with a $5 \times 5$ Lax
          Pair

Wang, Xiu‐Bin; Han, Bo

doi:10.11650/tjm/200806

Cited by 6 publications

(2 citation statements)

References 44 publications

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“…In this work, we focus on a physically meaningful nonlocal Sasa-Satsuma equation of reverse time type [39,40] equations (2) and (4) are two equivalent coupled systems, under constraint (5). By considering the derivation of this nonlocal equation, we can obtain the clear physical interpretation of its solutions.…”

Section: Introductionmentioning

confidence: 99%

“…For the CSS equation, Tianet al used Darboux transformation to study Dark-bright solitons and semirational rogue wave solutions [41]. Based on the nonlinear steepest descent approach, the long-time asymptotic behavior of solutions has been reported in [40]. Even though the CSS equation has been studied and generated much important work [42][43][44], to the best of our knowledge, its solutions with special initial solutions v(x, 0) = u * (x, 0) have not received much attention.…”

Section: Introductionmentioning

confidence: 99%

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Reverse-time type nonlocal Sasa–Satsuma equation and its soliton solutions

Yan

Chen

2023

Commun. Theor. Phys.

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In this work, we study Riemann-Hilbert problem and soliton solutions of a nonlocal Sasa-Satsuma equation with reverse-time type, which is deduced from a reduction of the coupled Sasa-Satsuma system. Since the coupled Sasa-Satsuma system can describe the dynamic behaviors of two ultrashort pulse envelopes in birefringent fiber, our equation presented here has great physical applications. The classification of soliton solutions is researched in this nonlocal model, by considering inverse scattering transform to Riemann-Hilbert problem. Simultaneously, we find that the symmetry relations of discrete data in the special nonlocal model are very complicated. Especially, the eigenvectors in the scattering data are determined by the number and location of eigenvalues. Furthermore, multi-soliton solutions are not simple nonlinear superposition of multiple single-solitons. They exhibit some novel dynamics of solitons, including meandering and sudden position shifts. Also, it has the bound state of multi-soliton entanglement and its interaction with solitons.

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Section: Introductionmentioning

confidence: 99%